Well, ya'll got me thinking a bit on this instead of doing what I'm supposed to be doing, so your punishment is to endure me rambling at you.
I think the Faunus situation should be looked at in two parts, long term and short term. Long term, I think ideally, they want to be integrated into society and treated as equals. Building Menagerie into an unassailable and unaccessible lost "elf" kingdom in some ways works against this, and I think might be something of a mistake. OOC we know that the White Fang at least has a large enough strain of Faunus Supremacy for it to be represented a bit in canon. I'm not saying we shouldn't go for low hanging improvements for Menagerie, but we need to keep Blake's actual long term goal in mind.
Now, I'm going to mostly be framing this as something Blake might consider in character, with what she knows about Remnant and her vague understandings of magic (as in, rather than "Black and/or Blue does X so how can we use X" and instead "X sounds like it would solve a lot of problems, I should look for how to accomplish X with black/blue/artifacts/etc".).
To give Faunus as a whole increased standing and military might, without separating them from the Kingdom's culture and society (Menagerie and White Fang), is going to be the kinda obvious. The thing shared across the Kingdoms is the Great War. The Great War and the resulting culture of embracing individuality to the point where what I'd be comfortable calling a majority of the actual combat power of the kingdoms are technically utterly independent mercenaries called Huntsmen (even if in practice a lot of them might serve in their respective kingdom's militaries, or would be quick to sign up in case of war). In canon, this was Blake's personal trajectory even, but Faunus are still a minority, and at a guess seem to be under represented in the hunter schools. I suspect this isn't due to overt bigotry, but systemic bigotry. Long term, vastly increasing the number of Faunus huntsmen and leveraging that to force change.
Now, from canon there is fairly good evidence that the low number of Faunus we see as huntsmen/huntsmen in training is due to systemic bigotry, that is, the Faunus don't have the connections or resources to apply competitively to huntsman academies. We know the main pipeline into huntsman academies are the combat schools. Combat schools which likely require tuition as well as the family being able to spare the young teenage labor, and its more likely for overt bigotry to rear it's ugly head at this level. And many graduates from combat school don't reach the level of huntsmen in training. Because I think the most important thing for aspiring huntsmen is personalized training from a huntsmen level instructor. Ruby herself was kinda trash despite attending combat school until she got personal attention and instruction from her uncle qrow. All of team RWBY comes from a background that would privledge them towards getting specialized and personal combat instruction. Ruby and Yang are the daughters of huntsmen, the Schnees are rich enough to buy any training they need, and Blake's family is well connected enough to ensure what resources are available in the Faunus community/white fang would be available for her.
So for a normal Faunus, they have barriers to get into a combat school, they have barriers to getting selected for personal attention once in combat school both due to being relatively disadvantaged and it being really easy for bigots to simply choose the non-faunus to give more attention to, and they are very unlikely to have the resources for any sort of combat tutor. So before the application process for the Huntsmen Academies even starts, Faunus are disadvantaged here. Ozpin can use his connections and influence to ensure the academies are as fair and meritocratic as much as he wants, but it doesn't matter because the Faunus don't even get to the starting gate.
So the primary barrier here is one of resources. Mainly huntsman trainers, because access to them is gated behind connections (existing huntsmen training family, friend's kids, etc), money for combat schools, or money for personal tutoring. So, this brings us to...
Short term goals.
A lot of Faunus are honestly stuck in an untenable situation. They don't have time to wait for long term improvement years down the line, they need help now. They don't have money to leave, and they don't have guaranteed employment even if they do at their new destination. And they can't just pack up and homestead because the real limit on settlements in Remnant is defensibility. There are vast swathes of Remnant that are straight up not settled because the land is too indefensible and that land likely has untapped resources. If Blake can acquire just two things, she can give places for Faunus to go that will also produce money which can be used to move more faunus, and get the resources needed to get Faunus into Huntsmen Academies (as well as the influence money brings).
First, she needs some way to make a settlement defensible against Grimm, ideally even when she's not there. It doesn't even need to be perfect, just enough to move it from "indefensible" to "a defensible mining settlement." I admit this isn't easy, but for any native of remnant it makes sense to me for it to be something of the holy grail of wish fulfillment magic powers. Making herself personally stronger is all well and good, but this would be something I'd think she'd keep an eye and ear out for. The question "can this be used to help defend against the Grimm" seems a Remnant universal. Even Faunus exploitation is wrapped up in that framing (cheap dust means more ability to defend against Grimm, therefore Schnee business practices are justified!)
Second, but less critical would be the ability to sense dust deposits. Dust is the resource that is always in demand, since it's the literal foundation of modern kingdom society. I'm sure there are other ways to accomplish this than Blake personally able to do it, but if she can figure out a method it will make things a lot easier.
With those two things, Blake would be able to find dust deposits that are unexploited due to poor location, set up a mining camp, and cheaply and safely extract the dust, while also providing Faunus who are in the worst position (Schnee dust mining serfs) a place to go where they're guaranteed employment. The cherry on top would be undercutting the Schnee dust company and ripping the market out from under them. This would also provide the resources needed for long terms goals for societal change, as well as providing powerful tools to influence Remnant society directly (money, dust, developing cheaper and more scalable anti-grimm defense solutions).
tl;dr: To change Remnant Society (without becoming a dark queen, beautiful and terrible as the dawn), Blake needs money and influence, dust is the easiest source of sustainable money and influence on Remnant, the biggest barrier to dust mining is finding and then extracting it in the deathworld that is Remnant, therefore Blake should be focused on abilities and magic that can defend against or circumvent Grimm, and that could prospect for dust across a wide area.
I think this a reasonable and IC direction for Blake to be working towards that's more coherent than pursing personal power and hoping that somehow gets her somewhere until such a time as she starts getting access to really Outside Context abilities that would make her re-evaluate.