In an email communication with Richard Koch, I followed his advice and that solved the problem.
Here are the steps:
“1. Go to ~/Library/Preferences and find "TeXShop.plist".
Move this file to the desktop.
Now restart TeXShop.
When Big Sur was first given to developers, TeXShop had a problem with tools in the toolbar. This was fixed before the release of Big Sur, but because the tools changed, there were problems with saving their state in TeXShop Preferences.
The TeXShop.plist file holds TeXShop Preferences, so when TeXShop restarts it will recreate a new copy with default values.
After that you may need to reset any preferences you have set before.
If this fails to fix the problem, you can quit TeXShop and replace the new copy with the old one on the desktop and return to your original preferences.
Note that ~/Library is the Library folder in your home directory, often hidden by the finder.