I've got autism, and struggle with anxious thoughts and low moods. Personally I have had a lot of time in which I've not been either in education and in work, and one thing I would fully recommend is to try and get out of the house at least half the days a week, go for walks wherever you can, stay active; dancing, swimming, cycling etc it doesn't have to be exercise, it can just be something fun that involves movement.
And then on the other hand, a low energy cost activity for days that feel tough, such as gaming or colouring/drawing.
If you don't feel ready to work, maybe try volunteering? I've not done it myself but I've heard you can choose the amount of hours you'll do.
So some of these things I have thought about, but haven't managed to do, such as getting out of the house every other day, and volunteering. One thing I did do was talking therapy over the phone, and join an online community through Mind called Side by Side. It's a lovely community, with people going through all different walks of life. It's nice to feel seen and supported, and also to learn from other people as to what they do to keep busy or cope.
Also maybe a self care diary? I have one that does daily intentions, daily self care tasks, and daily gratitudes. Might be nice to have at least one thing to focus on every day, and help you appreciate a day even if it is spent doing nothing but resting.
I hope you have a good gap year!