Ok, there's a lot to unpack here. The thing that people are saying about clinging to an identity has truth to it and it can hold you back.
However this is the way I look at it and interpret it. Depression is often an invisible illness. There are physical invisible illness too. Depression is a disability just like any other. It is very possible to a form of chronic treatment resistant depression that lasts your whole life. There is nothing dangerous about "normalizing" the fact that you can have a mental illness that will never go away. My 20s were awful because people who didn't know me were constantly trying to tell me this was a phase or I would "get over it". I didn't. Once I learned to embrace that and not listen to those people I started recovering further. However it still never went away, but I never expect it to go away. It is what it is, it's a pain sometimes, just like having a physical disability is, there are more steps to take, and more things you have to watch for but if you have some support and educate yourself you find ways to navigate it just the way someone with a physical disability does. As you get older you find more areas in life that are not for you, or you need more help in, and so on, and it gets better with age to some extent because of having more of these experiences to draw from and being secure about what your needs are and sticking up for them. It can be lonely as a lot of people try to tell you something else but if you know certain environments lead to hospitalization for you, you shut that out and stop engaging with that crap anymore.
So as someone with chronic TRD I look at what she's saying like this. When you're in "recovery" (I kind of hate that term with mental illness but it is what it is) your environment is very, very important to you. Let's forget the psych part of it now. Is someone with a physical mobility disability going to thrive if they're in a 6th floor apartment with no elevator that's not ADA compliant? No. No question. The disability is relevant to that situation because it's not a good fit for them and will contribute to worsening symptoms. If someone is physically in a wheelchair or physically has a cane or whatever someone may step in and be like, hey, yeah this apartment isn't ADA compliant, let's find you something else, whatever. But with invisible disabilities you don't have anything to go off of.
Now let's go back to that same analogy with someone with depression. People you surround yourself with, again, your environment, can heavily influence how this disorder plays out. Just because someone is "nice" and well meaning, it doesn't mean they are safe. Let me say that again. Someone can be the nicest person in the world, but not safe for you and your symptoms. This is not a value judgement, just like the apartment example is not a value judgement. It's not a good fit and it's better for everyone as someone with a disability that you have a good fit and environment for your disability as things are hard enough already.
But depression is an invisible disability. And depression is stigmatized. And now we can throw gender or other things into the mix. Maybe we don't want to tell someone about this, or people at our job, or whatever. There are different reasons for this. But at the end of the day you will run into disability related issues and people won't be able to contextualize them as disability related issues, and they will snowball, and you most likely will suffer as a result.
By being upfront and honest about your disability it's the same thing as having a wheelchair or a cane, although it's more stigmatized and less well understood in this case. In society we are at the point where we look down on people making fun of those that are physically disabled or not assisting them but it still happens to a crazy extent. A lot of the work is already done in that case. Even if people don't understand physical disability they are pressured at least to not be an asshole and pressured via ADA to help people out. The reality is that this does get a lot trickier and people who are really just surface level pressured by society and legal issues to help someone out in the workplace, well, you're going to run into a wall at some point with a physical disability too.
By talking about your disability it's a litmus test to gauge what people are "safe" for you. It will help you get further in your personal and professional life if you have a feeling for who will be helping you because they either have a better understanding (usually people personally impacted by going through it themselves or having a loved one) or someone who has an open enough mind to want to learn about it. The reality is that a lot of people don't fit into those categories. And in many many personal relationships and environments you will fail if you try to get people to understand who don't.
I'm guessing some of the people who are having a reaction to this article are people who just are in the camp of not being "safe" people and need to think about it more or spend time with a loved one who is affected by these things to understand this stuff further. Use the physical disability analogy I used to challenge your views on this subject.
People who don't understand this often think I'm passing value judgements on "perfectly nice" people. I'm not. I just need to cultivate the people around me in the same way that I need to cultivate a space that's physically accessible to me if I had a physical disability. The people you surround yourself can effect your emotions and depression is an emotional disability. If my health suffers when I'm around someone it's not going to do us any good for me to force it for their benefit or for appearances, especially when the risk for me is that I could end up hospitalized. You need to keep very strict boundaries as someone with a disability like this and since people don't contextualize it in the same way that they do a physical disability people are often berated and misunderstood for it, a bit like I see in the comments here. She needs to keep herself safe. It can be that you get wrapped up into the identity thing and I can't speak for her but being able bodied/disabled is just as relevant to your outward way of interacting to the world as is your gender expression or so on and you can't leave it off the table, nor should you really if you want to be healthy.