I honestly don't know a ton about coding, but I have a razer atheris that use for work and school, and I loved using the side buttons for productivity. I updated my MacBook Pro to Big Sur and it hasn't worked since. I found an app called steermouse that does the same thing as razer synapse without all the bells and whistles that razer synapse has.
I downloaded it off of homebrew (brew.sh), but it also works downloading it from the website.
Hope this helps those average joes just trying to get those side buttons working.
Apple won't let me attach the website, but just google steermouse and it's the first result.