I'm having the same issue on my M1 Pro MacBook Pro 14" 2021 running Sonoma 14.2.1. Firefox, Zoom, Discord, and Chrome none of them show up in System Settings -> Security & Privacy -> Microphone, Camera. I have tried using the following commands in the terminal:
tccutil reset Camera
tccutil reset Microphone
I have also tried reinstalling the apps which I want to grant access to. I have also restarted the laptop multiple times. Also, I tried deleting the following: /Library/Application Support/com.apple.TCC/TCC.db
Still, no luck.
Last but not least, I just updated to the latest version, i.e. Sonoma 14.2.1, and the issue persists. If it helps, I have System Integrity Protection turned off, so I will try enabling it and see if it fixes the issue, but I don't think that is causing the problem.