I'm having the same symptoms as described by previous commenters--that is, clicking on Finale causes icon to 'bounce' for a while, but it doesn't finish opening. It shows as open in the 'force quit' window, and can be forced to quit. But it's unusable without a GUI window, of course.
I'm using Catalina 10.15.7, and this problem has been intermittently present for a while, but has just escalated. In the past, if the problem showed up, I was always able to work around it by opening a specific Finale file, rather than just the program. But this morning, that stopped working. I did have a *very* extended power up this morning for some reason, and had to restart iCloud, so something in the OS is presumably involved. But it's not apps permissions.