Can't Close out of Time Machine Local Snapshots

What are you saying— if in the TM interface you can not use the cancel button or the Escape key to exit the interface?

Is this with an external drive attached or not attached?

Local snapshots work independent of an external drive.

About Time Machine local snapshots - Apple Support

Did you Try a SafeBoot https://support.apple.com/en-us/HT201262

to clear system caches and try again—

Takes noticeable longer to get to the login screen, does a 5-15 minute disk repair before it fully boots up, and certain system caches get cleared and rebuilt, including dynamic loader cache, etc. Log in and test. Reboot and test.

To find out if it's system wide or user specific, try this...

Open System Preferences>Users & Groups, unlock the lock, click on the little plus icon, make a new admin account, log out & into the new account.

Does it work in the new account?