It really doesn't though. We got this made from some of the most potent materials we've ever seen and spent a lot of money getting it done by a professional. It doesn't need to be at the height of it's power (which it certainly isn't) but it should still be damn good. If it's been significantly worsened due to the system changes then it needs to be retconned back to being fittingly powerful for it's narrative weight.
Looking at it again:
The basic problem (from someone who still doesn't really get the new system) seems to be it's debuffs, which seem pretty terrible. A 2 point debuff seems almost entirely pointless at our current level*, and it takes a minimum of 3 turns of successful attacks before qi drain even begins, with no real indication of how potent that drain is. Combine this with a low base health (with decent dodge) and assuming the +15 pen and +10 to hit for music arts are passive boosts to Ling Qi, we're probably better off keeping it back away from the fight for the passive boost rather than having it attack if we're fighting someone even close to our level or with a good offensive flying sword. If they aren't boosts to Ling Qi but the sword itself then I have basically no idea what they're there for. Otherwise the low base health and previous showings seem to indicate that it's unlucky enough to get hit it stays down.
For a sword who's description focues on terryfing whistiling and boundless screams of hunger it doesn't really live up to the hype. Raise the health, and power up the debuffs and Qi drain significantly and it becomes a lot better. Frankly you could remove the buff to Ling Qi's music (which isn't exactly exemplified in the description) entirely and slightly lessen the damage in return and it would still work well with it's thematics. Or have it actively Qi drain on hit as well as inflicting its drain over time.
*And will become even more so extremely rapidly, needing either extremely rapid number scaling up or the admittance that we wasted several thousand spirit stones worth of extremely vauluable materials.
So there are a couple of things going on with our weapon. I will not deal with the mechanics as there is an argument to be made that it's primary function (to debuff our enemies) has not been faithful updated into the new system. I have already voiced my concern with giving yrs more work already. Updating the mechanics of a weapon should not be done mid fight as that is just stressful to the GM and confusing to the readers.
Now lets talk about why our weapon seems weaker than other weapons. The first point is about the quality of the material used for the weapon. Here is a quote from week 44 part 1
"After some studying, yeah," Ling Qi grimaced, reading the auras of objects in such detail was hard. "It's a fourth grade material, right?"
"Only just," Meizhen replied. "Yet it is still above the resources one would expect of a new baronial clan. It is likely you will not be able to fully access the power of a weapon crafted with it, as you are."
So we are not even supposed to be able to access the full power of our weapon yet. We just are not strong enough. So as our domain increases our flying sword will increase in power as all flying swords do. Then we get another upgrade when we reach certain requirements because we are now strong enough to handle the material better. Therefore if someone has a flying sword made out of level 3 material they may only get one boost in performance per upgrade cycle. However we will likely get two.
Our weapon seems disappointing because we took a route most flying swords don't go. We went with a debuff style flying sword while most other flying swords have a much more concrete mission. Meizhen's sword is a stabby sword. We have not seen it do anything other than stab real good. Sun's sword is also a stabby sword. It likely doesn't stab as well because it also strips defense. Shen Hu's sword blocks damage. It blocks damage really well but we have not seen it do anything else. Ji Rong's sword blocks damage. It doesn't block damage as well as Shun Hu's sword because it has an emergency heal function.
So now what does our sword do with active affects. Our sword drains qi. Our sword boosts our own music. Our sword hinders spiritual avoid of enemies. Our sword has an aoe. These are 4 different effects with 2 of those effects effecting the enemy. Of course our sword is not going to be as good a stabbing people as other peoples swords. Have we seen any other sword being aoe? We can't get a sword that does everything well. We have a lot of cool effects in our sword. The cost that comes with that is that each of those effects are going to be weaker than if there was only one effect.
This sword is at level 1. This is not a sword that is meant to come running out of the gate and start smashing everything. This sword is meant to grow. What I am seeing right now is a lot of people being sad that we picked a growth focused sword and it is not being as flashy as they want it to be. Of course our sword is not as flashy as other swords. It has a lot of effects front loaded and therefore it likely has a lot of it's power back loaded. I honestly have no complaints with our sword. It is performing at the level I expect for a level 1 sword with so many effects unlocked at the start. I am expecting our sword to grow more powerful far quicker and for far longer than other swords wielded by our peers.
Point being, unless it's a drastic upgrade, it just won't cut it. This is made from an incredibly compatible material of fourth realm, by the finest professional CXR could find, to our specifications.
At our level, it absolutely shouldn't lose to essentially anything, as people flat out can't bring about the full power of something made from even better materials.
Yet it was weak before, and is just pathetic now.
Still waiting for our Domain to be useful, btw. Something as ridiculously restrictive as it should give a commensurate ridiculous bonus.
So I have a couple of problems with your statements here. I have talked some of them above but I will talk about them again here.
First, why shouldn't it lose to essentially anything at our level. For the following discussion I will use the word power to describe a resources used to get different effects for a flying sword. If we assume that at our level people can only bring out X amount of power from their flying sword regardless of material then everyone is roughly at equal power level when it comes to flying swords. However power can be applied in different ways. I would expect a sword that has no special functions or active effects to beat our sword at this current level. The reason for this is that they decided to apply the power of the flying sword differently than ours. The power has to go somewhere and if it is not going into active effects or special functions then the power has to go into the base stats and functions of the weapon. There is the same power for both swords and you can't just assume that someone is going to make a sword not make use of the power available.
Now both flying swords (ours and the other hypothetical sword) increase in power due to their owners leveling up. Now both people can handle Y amount of power from their flying sword. However the other sword only has X amount of power it can make. So it doesn't matter that the other student is able to handle more power because their flying sword only has X power. Sure that person has more control and is able to use their sword better but there is not a huge increase in ability. Now look at our sword. We can handle Y power and our sword can generate Y power. So now that power has to go somewhere and it will go into improving our sword in a far more meaningful way then the other sword who is still at X power.
Our sword would lose to the other sword when both people are using X amount of power because the power of the flying sword wasn't spent on combat specs it was spent on unlocking different effects. However our swords growth rate will be massively higher than other swords that our peers own because of it's massive quality.
Now on to the next thing I have taken issue with in your post. Is our domain weak? I don't really know. Why don't I know? Because we don't have really any one else to compare to.
Meizhen likely has a lot of different green level arts slotted into her domain already which makes it look really powerful. That is the benefit of being a member of a ducal clan with a clear vision of what domain they want. She likely had a great deal of arts that ended at green 1. We don't have either of those benefits.
What was Sun's domain? Did we see it used?
How about Cai? How strong is her domain?
We have the curse of knowing exactly what our domain does in terms of numbers. That makes it really easy to say "Man those numbers look low so our domain must be weak." But we just don't know that. Remember we have a level 1 domain right now. It is not suppose to be overwhelming. Meizhen is the outlier here. Most people do not have domains as strong as hers at her level.
Now lets look at our domain. When we look at our domain the relationship requirement of being a 4 to get benefits seems super restrictive. However you know what I don't see in that restrictions list? A limit to the number of people we can support with our domain. That seems broken. It really does. But Nesh you cry, we simply don't have the time to maintain that many level 4 relationships so there is a hard limit to the number we can support! "Ahh" I reply, but what about arts. We have seen arts do some crazy things. Is it too out there for there to be an art that temporarily boosts relationship levels? I don't think so.
I image that diplomats might use such an art. In fact perhaps that the type of effect that blood moon bro used on us when we first met. Thus we neatly get around our restriction. (The fact that Cai is thinking about making us more of a diplomat instead of spymaster makes this route to breaking our restrictions way more appealing.) A limit to the number of people a domain can affect is much worse than a limit to the type of people our domain will support.
Instead of looking at the limits of our domain and thinking about how weak that makes us we should be looking at ways we can break those limits and therefore our domain.