As I said, I understand there are reasons why Hazel thinks that way, even if I wasn't considering all the points you've laid out here. It's just...
Hazel's magic thus far gets result that are, for the most part, the same as or similar to witch/wizard magic (traveling long distances, writing in the air, etc) even if the exact mechanisms are different. Both are fundamentally physics-defying forces. Both require an inborn and inherent gift. In that situation, to me it looks like the two are either very closely related or actually the same thing, and absent other evidence (i.e. learning of the existence of a magical species that can have two powersets, humans with completely separate gifts to magic, etc) that should be the assumption operated under until proven otherwise. Occam's razor- the simplest explanation is most often correct. And here, the simplest explanation (to me and the way I think, at least) is that she's using a known and existing ability slightly differently rather than having a completely new one.
And yes, I know I'm looking at this from an outside perspective, with a great deal more experience and knowledge than Hazel, and without having grown up abused for being different. It makes perfect sense that Hazel wouldn't think this way- she's a hurt, lost child trying to find her way in the world and with very limited access to information, not someone looking at it from the outside from a clinical perspective. That doesn't change the fact that my gut reaction is something along the lines of 'please, stop for a second and think', plus a wince in sympathy as I imagine how she'll cringe when she looks back on her early assumptions and complete confidence in them when she eventually gets proven wrong. It makes sense for the story, but it still makes the parts where she talks about druid magic as if it's completely separate a touch painful (just replace 'druid magic' with 'chi' or 'psychic powers', and you get basically the same effect).
As for why the difference between the two options (primal magi vs different magic) matters, that ultimately comes down to two things. First, the stuff I've outlined above, about how not considering an obvious possibility makes me wince to read about. Second, a lot of the time, the better and more accurately you understand something? The more you can do with it and the more deeply you can dive into it. It's not always the case, but if it applies here then by assuming she's using something different to witch/wizard magic Hazel is potentially putting artificial limits in place on what she can do, and limiting her ability to apply what she knows from witch/wizard magic to her own. And while that's far from an immediate concern or issue- this clearly isn't a story about Hazel powerleveling and becoming teh gr8est witch EVAH, or diving deep into the fundamental laws of magic- it still places blinkers on her.
TL;DR: I don't think there's any actual problem with what's been written, and it makes sense IC Hazel thinks and assumes the way she does. I still react to it with winces.
As you've said, I would assume that they were a form of language. And in this example, for me at least that's what access to magic is- the raw ability to communicate rather than the form it takes (i.e. magic is the ability to write, witch/wizard and druid casting styles are the individual languages, and the fundamental rules of each style are the spelling and grammar).
My first reaction to this entire post went something along the lines of "wait, what?". After what, half an hour?, I think I understand what you're saying, and if I'm right there was a MASSIVE misunderstanding or miscommunication somewhere.
Let's start from the basics. Some humans have magical abilities. Not all, but some. Let's call what they can do "human magic"; i.e., all magical humans use human magic.
Wizards are a
specific subset of magical humans. They use wands and, by their own admission, cannot cast spells without a wand. When I talk about "wizard magic", I am speaking
specifically about casting spells through a wand,
NOT human magic as a whole. Just like when I say "wizards", I am not talking about magical humans as a whole. I am talking about this specific culture.
Hazel/"the druids" is part of a
different subset of magical humans. She does not need a wand to cast spells. BUT, she still uses
human magic just like the wizards do. Her means of accessing and forming it is just different, as proven by her experimentation.
That is why I made the language analogy. Wizard magic and Hazel's magic are as unrelated to each other as French is to Aztec. But that does not mean that they aren't both types (or, if you prefer a different word,
manifestations) of human magic with different rules and restrictions just as French and Aztec are both human languages but with very different grammar. It also does not mean that someone can't be "bilingual"; Lily certainly was since she could both use a wand and could do magic without a wand, and
Hazel knows this. It's part of the reason she is in Hogwarts in the first place, to see what spells she can adapt to her way of casting spells (or to continue the analogy, to find "words" she can translate from one language to another).
The only thing I can think of for why you think that I'm implying that Hazel isn't using human magic is some of her earliest musings about how the folklore she has read talks about druids "pulling" or deriving their magic from a connection nature. Theories she came up with before she knew for a fact that wizards even existed. I also need to direct you then to two chapters ago, where Hazel was reflecting on the difference between druid and wizard magic now that she actually has some information on wizards (again colored for emphasis):
Did it have to do with where she drew her powers from compared to wizards? Druids, as best as she could determine from folklore and her own experience, derived their magical powers from nature. It was part of why her magic worked better on living things and how she had turned a simple tree branch into a living staff using nothing but meditation. It was also how she was able to communicate with wild spirits, like when she bargained for her fairy lens and when she asked for help tracking the magic boar alongside Grégoire.
But if her magic ultimately came from a connection to nature, where did a wizard's power come from?
As Professor Flitwick started describing and comparing how the motion of a wand directed the 'flow' of a spell, she could not help but mull that over in light of her question. Was the reason wizard spells could be so unpredictable due to the wands themselves, perhaps? She could not help but recall that Mr. Ollivander had made it clear that wands had their own thoughts and made their own choices. Was that the difference, that there were in essence two minds of a sort involved in any spell a wizard wanted to cast?
Might it be that a wizard's power came from a wand or other magical item, and that was why they were so dependent on wands to the point that they couldn't cast spells without one? It sounded like a simple enough explanation, but the books she had read mentioned that underage witches typically had uncontrolled bursts of magic before they were given a wand. That meant it could not be magic pulled from an object.
Hazel frowned and tapped the page of her notebook with her pen. When something was not working or was not making sense, she had learned that the best way forward was to go backwards instead and look at where she might have made a mistake. Maybe it was not that the druids' power originated from nature but instead were directed or channeled through it? When she meditated, she was giving some of her magic to the world and taking some of its magic in return. Her own spells, then, was not purely hers. It was hers and nature's combined.
So she's still refining her theories about what magic IS and where it comes from, and has already moved to the theory that I explained above.
Oof. Moving on…
Hazel's unique magic isn't a problem to be solved, neither is the lack of a wand or her being mute. But what could be done is clearing up the misunderstandings, starting with her being a runaway because she had been abused by her relatives. She could explain the magic she has learned already, she could demonstrate the magic tools she crafted, she could tell them about her travels.
In turn she could be told about her vault in Gringotts, about her parents, about her status in the wizarding world and related stuff.
You know, communication and exchange of information. People assume a lot of things about her, she assumes a lot of things about people and neither side is correct. If the school is being informed about her limitations, then they can accomodate her. Although failing to allow mute people to enter the Hufflepuff common room is a mark against them. That's basically the one thing they definitely knew about her from the start.
Right now it looks like Hazel doesn't care to do any of that, she even accepts that the other kids are trashtalking her and assume she's a squib. Something she could clear up quickly if she wanted to.
Yes, I completely understand that she's broken, different and not the typical child. Anyone else would look for help after being locked out, Hazel simply accepts it and is fine with sleeping in a corner somewhere. That doesn't mean she should treat every problem like that... it's not like they stop existing after being ignored.
Hoo, boy. If you want all of these topics to be addressed, either individually or with other characters, you are in for a LOOOOOOOONG wait. Some of this stuff won't pop up for literally a couple of years.
The only thing I want to address specifically is that you said Hazel could clear up the misunderstanding about whether she's a squib quickly "if she wanted to". I bring this up because I think it's important to understand that she
doesn't care. Whether the wizard kids think she is a Squib has no impact on her ability to use magic. I brought that up in the last chapter to make sure it was clear.
Is this going to further ostracize her and keep her as an outsider within Hogwarts? Probably. Will it keep her from making some friends? No. Will she ever care about the opinions of wand-wavers as a society?
…Not sure because that depends on the muse, but all signs currently point to
no.
Moving on, though, I really want to talk about Peeves. I'm probably reading way too much into this, but there have been a number of fics that have tried to delve into Peeves' nature as distinct from ghosts, boggarts, and other spirits. After Hazel's interaction with the spirit behind the Sorting Hat, I've been thinking about Hogwarts' connection to its spirits, and I'm both curious and concerned about how this will impact Hazel's relationship with the school itself.
My first reaction was to guess that Peeves in this story was another manifestation of the entity behind the Sorting Hat, and was expecting Hazel to recognize it when it seemed ready to drop the Peeves persona:
Wait. You think that Peeves… and the Sorting Hat…? Oh,
hell no. They are two ENTIRELY different entities.
Peeves is a poltergeist. He is not part of Hogwarts; he is a
guest within the castle at the pleasure of the Bloody Baron and the Headmaster/Headmistress (not that the individuals who held that position over the last several centuries know that). That's why threatening him with the Bloody Baron's displeasure can tend to make him behave or at least go torment someone else.
The entity that is referred to as the Sorting Hat is… something else. I can't see the Bloody Baron ever trying to take that entity to task over anything, but if it did happen? Smart money is NOT on the Baron coming out on top.