Arch is great. You’ve kinda dipped your toes in it with Manjaro already. I recently moved to EndeavourOS with BTRFS for my gaming computer and couldn’t be happier. I could have done stock Arch but I honestly didn’t care enough to. EndeavourOS has great sane defaults and no bloat. And you can pick almost any DE during the install. Spin up a VM and give it a try if you can.
I can’t speak to MATLAB though. But all the others you mentioned I also run.
The only issue I have right now is the half screen flickering with GNOME and NVIDIA drivers. But I just ignore it.
You should only have to backup the Postgres database. But it won’t hurt to have a copy of your compose file as well.
This GitHub issue has the steps you should use. And answers all your other questions too.