I'm used to use Brave Browser on Windows machine and also on Linux and Alby works fine on both platforms...

This is maybe something like classic IT advice. but try and you'll see:

- Check if Your Brave Browser is up to date.

- Try to install some any other extension (for example uBlock Origin, Privacy Badger, DuckDuckGo Essential), if works at least something of this...

- Maybe - try to create a new (empty) Brave Profile and try to install Alby in it... 😉