I finally found a solution, which might work for other Zoom issues. Since I had been using 5.8.0 to get around this problem, I was concerned when Bort posted that, in November, version 5.8.6 or higher would be required. So, I asked Bort what to do. He at first suggested that I start a ticket. I explained that I didn't seem to be able to start a ticket, because next to the ticket button is a statement that Basic and Pro users can only submit tickets for billing issues(!). Bort took pity on me and submitted a ticket on my behalf. Within a day Andrew H. got back to me with the following instructions:
... from Zoom Support ...
On both of these Mac's go to your desktop.
Click on the 'Go' option in the top left hand Mac menu.
Hold down the option key and select 'Library'
Open the folder 'Application Support'
Delete any folders in here titled 'Zoom'
Go to Applications in your finder and make sure Zoom is missing, if it's still here delete it.
Next, reinstall from zoom.us/support/download
Open System Preferences and then Security and Privacy.
Make sure Zoom is checked on for Camera, Mic, and Screen Recording.
... end Zoom Support...
In addition, I used the Finder/Go/Go to Folder command to look in all the following and remove anything with Zoom in the title:
- ~/Library/Caches
- ~/Library/Logs
- ~/Library/Cookies
- ~/Library/Saved Application State
There were a few, though I'm not sure how important this step is. Then I emptied the trash, restarted, and followed the reinstall instruction above.
This did the trick! These actions get rid of files that may be corrupted, though since both my Mac Airs had the problem, it's more likely that some of the remnants of earlier installations were incompatible with 5.11.3 and following.
I also asked Andrew H. if it's really true that I can't submit a ticket as a Pro member. No response yet.