Lightroom CC Classic has been unusable for months

Sous like the catalog may be corrupt..

1. Copy your catalog to another location. Note I did not say backup, that imply's using the backup capability in Lightroom that you state does not work. Just copy the catalog, preferably to a different drive, and preferably to multiple drives. The following just might break your catalog. Steps others might recommend might break this catalog (it sounds like its on deaths doorsteps)

2. If you can keep Lightroom up long enough, go into Catalog Settings, and change the backup setting to anything other than when Lightroom exits, i.e. do not allow an automatic backup just now (remember to change it back later)

3. In Preference change how Lightroom starts, have it prompt you:

Now, I am pretty sure their is a keyboard option to do this when you start lightroom, just can not remember it.(followup, alternate, hold down CNTRL key when clicking on LR icon to start in this mode)

4. Close Lightroom, wait a few seconds, and restart. You should be presented with a dialog screen:

Tell it to accomplish an integrity check. Note this just might break the catalog even though its supposed to. It might present a clue as to what is going wrong with the catalog. Key word might. Incidentally some recommend accomplishing an integrity check at start up instead of upon closing as if you do that upon closing and the integrity check fouls the catalog up, it then royally fouls up the backup.

NOTE, you could also choose to create a new catalog and see how the new catalog behaves before doing anything hazardous to your apparently ill catalog.

5. An additional consideration, and I cannot prove this, is to delete your presets CACHE (careful, get the correct folder)

6. An additional diagnostic, is to start your computer in safe mode and see if Lightroom behaves better, if it does, then some OS or Hardware issue needs to be addressed.

7. And what about your anti virus or internet security? is it stomping upon your catalog?

8. Oh, and have you reset the preference file?

Some references

https://www.lightroomqueen.com/catalog-corruption-cause-prevention/

Troubleshoot Adobe Lightroom problems, issues, or bugs

https://www.lightroomqueen.com/hurry-up-lightroom-the-best-speed-tips/  (third paragraph from bottom "And finally, a little logic.  Virus protection constantly scanning the same files that Lightroom’s trying to use will slow you down.  Consider excluding the catalog (*.lrcat), the previews file (*.lrdata next to the catalog), and the ACR Cache (check the Lightroom Preferences dialog for the location) from the live scan, and perhaps the images themselves.")

Replacing the Lightroom Preference File – Lightroomers

Resolving Buggy Behavior in Lightroom: How to Reset Preferences - YouTube

Preference file and other file locations | Lightroom Classic CC and Lightroom 6

The first thing I would suggest to TRY would be to disable the graphics processor in the Lightroom preferences to see if that makes a difference.