You can definitely rule out some things (go to the terminal).
# ps -ef | grep -i firefox$
502 56288 1 0 11Mar21 ?? 207:43.89 /Applications/Firefox.app/Contents/MacOS/firefox
USE the executable name and pass to
# file /Applications/Firefox.app/Contents/MacOS/firefox
/Applications/Firefox.app/Contents/MacOS/firefox: Mach-O 64-bit executable x86_64
So if that gives you x86_64 it has to be running under Rosetta - it's got only x86_64 architecture (the pre-M1 one).
On a M1 machine some things ship with universal binaries - for instance do the same thing for Safari and I get something like this (sorry machine is air-gapped .. this is TCP-over-ME so may not be 100% correct :-)
# file /Applications/Safari.app/Contents/MacOS/Safari
/Applications/Safari.app/Contents/MacOS/Safari:Mach-O universal binary with 2 architectures: [x86_64:Mach_o 64 bit executable x86_64][arm64e:Mach-o 64-bit executable arm64e]
.. and then proceeds to give output that is for each architecture ... According to Apple it will "prefer" arm64e.