AddingAn alternative solution to crgarridos and Nic and mayby as a different solutionNics that worked for some:
I had the same problem: The prompt to grant accessme is to camera and microfone didn't come up for Slack and other appsreset NVRAM
/PRAM
.
My System Integrity Protection (SIP) is (and was) disabled and should stay that way (running on Catalina-Patch).
Finally I reset NVRAM or PRAM (https://support.apple.com/en-us/HT204063). That did the trick for me. SIP was diabled at all times.
I found the solution in this article. Thanks for that: https://ericasadun.com/2020/05/04/catalina-permissions-chrome-zoom-etc/article.