You don't have to make giant changes all at once to get healthier, it starts with simple things like eating less or going for a 2 minute walk to the end of your driveway and back, and then build from there.

I've been in a similar spot as you of being so depressed and anxious I didn't leave my house for weeks at a time, and being over 320 pounds.

Currently i'm down to 215, and while I do eat much healthier and walk 5+ miles a day as well as regular exercise, it started with small changes of eating a single bacon cheeseburger and medium fries instead of a double bacon cheeseburger and large fries, or walking my dog for 10-15 minutes a few times a day.

My point is, find literally any positive change of any size you can make in your life and start doing it, then once you do that, find some other way to build on that with the next step of that chain you chose and keep building.

I get that the deppression and anxiety makes the all or nothing thinking of i'm either a lazy piece of shit that sleeps all day, or I go to the gym for an hour everyday seems like the only options, but neither extreme is really sustainable, and by setting small goals you can obtain it makes you feel better about the depression and anxiety along the way.