For me the best way to run Firefox on Debian based system is to download the compiled tar and extract it somewhere in my home dir. This way I get update through Firefox itself (like on Windows/MacOS).
I believe the 'proper' place to install it would be /opt. You can then give yourself edit permissions for the firefox directory so that firefox is capable of upgrading itself when you run it.
https://www.ghacks.net/2022/03/17/each-firefox-download-has-...