I have been involved at a management committee level of my local animal rescue for nearly ten years. During this time, we have done over a thousand adoptions of cats and dogs to local families, and I've seen and learnt more than I would have thought possible back when I first started to get involved.
All I wanted to say is that sometimes it just doesn't work out. It's no-one's fault, not yours and not the cat's, sometimes it simply isn't what people think it will be. Which sounds like the issue here. And that's ok, it happens. I want to repeat, it's no one's fault. Life can be complicated sometimes.
Ultimately you need to make the best decision for both the cat and your mental health. From your original post, it doesn't sound like your cat has got any behavioural issues as such, it's just that his very presence in your life is just that little bit too much for you to handle right now. And it is ok to feel like that. If you are unable to care for him, feel overwhelmed by him, etc, then I would contact the rescue that adopted him to you, explain the situation, and ask if they can take him back into care. I believe animals know when they have found their forever home (I have seen some very weird and spooky things over the years, lol), so if you aren't feeling that you are the forever home for this little guy, chances are he already knows this too. He does deserve the opportunity to find his forever family if you believe it's not you, so I would ask the rescue if they are willing to take him back.
Sometimes animals can really help with our mental health, and sometimes its too much. Personally speaking, I wouldn't get through my depression episodes without my dogs, but I live on a large property and work, so it works for me personally - if I lived in a small flat, it most likely would make things worse! If you feel you would still like a connection with animals, perhaps you could volunteer once a week to walk rescue dogs or play with rescue cats at a local shelter if possible. I know this helps many people who want the connection but aren't able to have fulltime animals.
All the very best, I hope things improve for you.