on f-droid there is a hardened firefox fork: mull
Btw, modern cars are often nightmare for privacy. Mozilla has recently posted about it.
However, I saw on github that someone made android auto work with microg!
don't recommend manjaro. instead - vanilla arch or endeavour os
I'm not sure if using Librewolf on desktop or Mull on mobile counts but they are pretty good hardened forks of Firefox.
Firefox is great but the downside is that it isn't as private as browsers I've mentioned by default. Still, it is solid choice from privacy perspective.
Redlib