Should I format my disk when reinstalling macOS?
Yes - it’s the perfect time and often sets you up for the best experience.
Your question is hard to answer absolutely since it does take a bit more time and some people don’t have confidence or skill in their backups. You can’t get the image Apple provides since it has non-registered versions of the free apps to claim. But on all the supported OS (N-2 with N being Catalina on October 1, 2020) are free and you can download them easily after an erase. I especially recommend an erase install if you want to be sure the hardware isn’t the cause of issues. You don’t have a better test than this in my experience.
Installing on top of a corrupt partition / volume / system won’t fix that, but will restore the OS cleanly. Make a backup and check your important files are intact on the backup and erase-install is my go to move.
You get to test a clean slate and then do the erase a second time if needed then restore files back. It takes a little extra time, but you never have to redo a step and build confidence the hardware is good sooner than an overlay install.