I haven't been in your situation, but I'm the same age and if my wife and I separated for whatever reason, I suspect I probably would be. I find being social and trying new things to be incredibly difficult. So it's something I've thought about. Personally I would not try to adapt to being alone, but rather I'd try to find & meet new people.

I would suggest trying to find in-person employment, whether that means changing to a job with a local office, or finding a co-working space to go in to. Then go in to the office every day. You can do less frequently than that, I guess, but it will just increase the time it takes for bonds to form. It turns out if you're a decent person to be around, it's almost impossible to not make social connections if you have lunch with the same people 5 days a week, 50 weeks a year. For both my wife and I, the vast majority of our friends are people we met at work, or through people we know at work. There are other ways to make friends, of course, but work is one of the faster & more reliable sources IME.

My other suggestion would be to get back into the dating pool when you feel more ready for it. It's an environment where everyone is expecting to meet new people and try things out and maybe things don't work and that's OK. I think dating is a lot different in your late 30s than it is in your early 20s, much more casual & experienced and hopefully less stressful. Even if it doesn't work out romantically, it's a way to get some practice meeting people and talking about yourself, and maybe make some new platonic friends and get out of the rut.

People suggest hobby groups and volunteering, but I dunno, I've tried that and it never really works out for me. I'm very shy and have a hard time inserting myself into an existing group. The infrequency of meetups also means it's hard to give the time for bonds to form, especially for someone fairly aloof like myself. That said I have started going to a weekly Fighting Game tournament and that might be working out. We'll see.

Just some ideas from my own ruminating on this issue. Hope you can find something that works for you.