Logitech mice usually come with "Logitech Options" which controls the button features. Did you previously set up any program specific settings for Firefox in the Logitech options 'All application' setting?

No there's no Logitech software running anywhere on the Mac. It's just using the built-in default mouse support. Like I said this is uniquely and specifically an issue with Firefox.

Try downloading the latest version of "Logitech Options" for your OS. https://support.logi.com/hc/en-150/

Near the bottom of the page there is a button "Downloads and apps" click it and on the next screen you should see the list of software to download. Click the "Logitech Options" icon (screenshot) and it will offer you the version for your OS.

Once it is installed you can change the Logitech mouse button assignments for specific programs, without affecting the normal button operations for non-specified programs.

e.g. When I watch Youtube videos, I use the left and right wheel press to control volume levels. But in general applications those same buttons default to control scroll left and right.

It bothers me that your solution is to install more software and generate a hacky work around instead of just finding the setting that is unique in Firefox.

That being said, The logitech software says that I do not have a compatible device for the software. Its just a Logitech M510. But even more fun, I plugged in an old USB wired HP mouse and guess what? Exact same behaviour. Once again - this is a Firefox issue.

I am surprised that you were told that the M510 is not a compatible device. This is the same mouse I use, with the Logitech Options software (see screenshot of my post 5/20/20 5:59PM.) it is available in MAC from OS X 10.8 to MacOS 10.15