After 4 days of trying, I finally discovered a fix. This is in regards to the horrific snafu between HP & Apple resulting in HP printers being unable to print with macOS Catalina or Mohave. If you have an old HP printer the following might help you.
I've tried all the fixes I could find for the last 4 days on many message boards and could not get a fix to work until today. This took about 6 hours of trial and error. I have a 12 yr old Color LaserJet 3600 and a 10 yr old PhotoSmart Premium multi-machine. I run a MacBookPro with Catalina 10.15.7.
Most fixes for old printers talked about deleting the printer in System Preferences/Printers & Scanners, then deleting the HP files in Library/Printers, rebooting, then downloading the HP Drivers Pkg 5.1 and then re-installing the printer thru System Preferences/Printers & Scanners. I tried multiple versions of that scenario and nothing worked.
My last idea before I gave up entirely worked. Here's what I did:
Try to print something again and when one of those annoying error boxes ("xxxx.xx will damage your computer") comes up, you have two choices -- "Show in Finder" or "OK". Choose "Show in Finder".
That will take you to a hidden part of the Library which will show you that file inside a hidden HP folder.
Now with that Finder window still open, I went back to System Preferences/Printers & Scanners and deleted both HP printers.
THEN I went back to the open Finder folder to DELETE THE ENTIRE "hidden" HP FOLDER. That's the key. (Every time I tried it before I simply went to Library/Printers and there was only a single file to delete for each printer.
Once I had that entire hidden folder deleted -- the rest was easy.
Reboot again just to make sure everything comes up clean.
Open System Preferences/Printers & Scanner and wait a bit. Both my printers appeared on their own. (They were both attached via USB.)
When I tried to print to the first printer I was encouraged that no pop-up errors came up. However a dialog box did appear which asked if I wanted to download drivers direct from Apple. Definitely YES.
It took a minute for those to download.
Then I had to click on the printer icon in the task bar because it couldn't print without the new drivers. (I might have this part backwards because it's done now and I don't want to recreate the entire scenario. Maybe you have to click on the printer icon first to see the message asking if you want to download drivers direct from Apple. One way or another, it worked. You need the drivers direct from Apple.)
This snafu between HP and Apple is a nightmare scenario for HP users around the globe. I called HP support this morning and got no help from a very nice rep who basically said printers that old weren't worth the effort. I was ready to give up after that phone call, but that's when I had that one more idea about wondering where that "Show in Finder" choice took me.
Once I had my first printer running, I just had to reinstall the 2nd printer in System Preferences/Printers & Scanners and go through the same process to download drivers directly from Apple.
Good luck to everyone who is still struggling with this.