So this might not be the right place to ask this question, but I've no idea where else to post it.

So several months ago I've met this girl on tinder, we quickly clicked and started seeing eachother regularly. After a while she admitted to me that she is diagnosed with paranoid schizophrenia and takes medication for it regularly. Now I was totally fine with this, to be fair I too have my own mental issues (depression, anxiety) which I'm also taking medication for.

Everything was going great, now I'm not that socially skilled, but I can recognize when somone is showing signs that they like me, and she definitely was. The problem is when I asked her for something more serious, at first she said she needs more time, and after another 2 months, I asked again and we had a long conversation where she rejected me, giving a reason that she just doesn't feel anything, that she just isn't sure of anything and that we can just be friends. I've asked her to clarify is it just me or does she feel like that in general, and she sad that she feels like that in general, that after we finish talking/messaging she just doesn't think about me, etc.

Now I really like her, but I'm also an adult and a rejection is a rejection, just move on.

But what keeps bugging me is that by any metric she behaves as if she likes me, and I'm just wondering does her lack of any feelings and uncertainty come from her diagnosis and treatment?

If so should I try and persevere, without pestering her obviously, and see where it goes, or if I should just cut my losses and move on?

I would really like the perspective of somone who is going through or has gone through similar things, on either side.

Yes, I'm also aware of the possibility that she just doesn't like me at all and that I should just move on and reinstall tinder. :D

TLDR;
I like a girl with paranoid schizophrenia who say that she just doesn't feel anything at all, and I want to understand her feelings better.