macOS Catalina upgrade install with macOS Yosemite is stuck at macOS Catalina will be installed on disk

I'd suggest patience proportional to the time since your last backup.
Catalina will reformat the drive into new partition types. Interrupting that is going to mean starting over.
If you're lucky, the time it's taking is simply the time needed to reformat. macOS since maybe High Sierra or Mojave really expects to be running on an SSD, so there's going to be considerable additional time penalty whilst it does this conversion on an HD.

If your backup is good, you could consider dumping this attempt & start over with El Capitan, which is considered minimum OS from which to jump to Catalina. I'm somewhat surprised the installer didn't prevent you from going ahead, though I've never attempted to jump this far myself, so I don't know how the installer should react to the attempt.