Finder windows not functioning properly (Catalina)

All of a sudden Finder windows on my iMac became partially unresponsive. I say "partially" because there were still some things I could do, but many others I couldn't. One clue as to what was happening was that every time – and everywhere – I clicked the mouse, whether on an open window or on the desktop, a contextual menu would pop up, as though I had click-pressed the Control key (and no, there wasn't anything resting on the key!). Things I can/can't do are as follows:

• I can't move windows around the desktop.

• Buttons in dialog boxes don't work, although some respond to keyboard commands such as the initial letter of the button name. Checkboxes, radio buttons, etc. don't work.

• I can't open windows, files or applications by double-clicking on them, but I can open them via the Dock.

• Menu items (in the Menu Bar) seem to work okay so I can open individual System Preferences although I can't configure anything in them.

• Applications seem to work until I open a dialog box; for example, links in Safari mostly work, although not buttons/checkboxes in pop-up dialogs.

• In window tabs (and Safari tabs) I can only navigate between them by using keyboard shortcuts, not by clicking on them.

• I can only close windows and tabs by pressing Cmd-W (which I do normally anyway, so not a big deal).

Things I've tried to remedy the problem:

• I deleted the Library Preference files com.apple.finder.plist, com.apple.desktop.plist, and com.apple.mouse.plist files (but not any others) and rebooted. No joy. I didn't want to delete any more plist files because I'm not sure what unintended consequences that would have.

• I booted in Safe Mode, where the problem also existed.

• I attached another keyboard and mouse, but that didn't work either.

• I tried to install the latest Catalina update (10.15.5) but, in the installer, I couldn't get past the Continue button as it didn't work.

I wonder if the problem is something to do with third-party apps such as Default Folder or TotalFinder but why did it suddenly happen now, when neither of those have been updated recently? Also, since I had just activated "Secondary Click" in Mouse preferences, whether that's the problem. But if so, how to fix?

I'd very much appreciate it if anyone could offer insight into the problem – and hopefully a fix.

Thanks.