I'm a lot older than you (57) so I may not be the best advice giver.
I laid in bed for literally two years. Didn't even work. That's how depressed I was. We tried everything basically except ECT. It was just awful.
I never was that actively suicidal but I definitely did want to escape everything.
Time just passed and I got better. I am still not great, but things are better.
I think your plan of exercise, nutrition, and meeting people at sports things, etc. sounds great. That sounds really healthy and like a great plan.
Do you have the energy to start a routine at all?
For example,
just start packing your lunch and making your bed for a week. This might sound dumb, but maybe it would get you started.

Believe me, I have been where you are. I understand and sympathize.