I think I may have found one answer to the slowdowns.
When it occurred on my machine, I had about 50 browser tabs open in Firefox, and perhaps 5 open in Safari. For privacy reasons, I used Firefox and set it to auto-delete cookies and cache when the tabs were closed. I only used Safari for forums and accounts that required a sign-in. Firefox was what slowed down first and then it spread throughout my machine. I quit every program and restarted and the issue was still there.
I used my Time Machine backup of my home iMac to restore my office iMac to Catalina, and also give me access to my important files in case the home machine took a dive. It works just fine, even though the office iMac is 5 years older.
The home iMac kept crawling slower and slower, like if it was going to thermally overload, but there was no excessive fan noise. Finally, the thing froze and then blinked out and rebooted. When it came back up it was running fine, except there was a "problem report" window open. I haven't clicked the "Send to Apple" button yet, because I have no idea what info that might pass to them.
Since then the computer has not given me much trouble, aside from the occasional "I'll think about it" when I click in a window and start to type. I've also noticed that Safari, when I click on a link, will revert to showing the sending page in the title bar until the linked page has loaded. This makes me think I didn't click the link and I do it again, and then the page load screws up. Finally, page loads have screwed up occasionally, reverting to the old text version of a given site until I click it a second or third time.
Based on this I think that memory issues caused by the browsers are a major issue. Safari isn't as bad as Firefox.
One last detail I should mention is that the most recent updates of Firefox have been nearly unusable for me. Lots of sites are broken or missing objects. I'm not happy with how Apple took cookie management out of the users' hands a few versions ago, so I really want an alternate browser that gives me cookie control and also mitigates a lot of the security risks. There's really nothing out there, so I'm stuck with Safari.