My Catalina update is stuck! What to do?

Try Safe Mode as per > Use safe mode to isolate issues with your Mac - Apple Support

If that doesn't help, then I would try Reinstalling macOS and Restoring from my Time Machine backup.

How to reinstall macOS from macOS Recovery - Apple Support

If you can not see your Macintosh HD startup disk or fully install macOS onto it, then it sounds like you may have a hardware problem that needs to be checked out.

Hold the power button until iMac shuts off, wait a minute, then press the power button and turn the iMac back on.

I've tried this 3 times now (I'm stuck installing on a Mac Mini) and it gets to the same stage each time but doesn't progress from there. "Setting Up Your Mac - Setting up..."