In my experience with a new MacBook Pro running macOS Monterey, Firestorm and Alchemy require a security override during installation when GateKeeper blocks launch (System Preferences -> Security and Privacy -> "Open Anyway"). Subsequently, the apps never cause MacOS to prompt the user with the dialog box to give permissions for the microphone. Worse, the apps never get registered/added to the list of applications to tick and untick at a later time in the System Preferences > Privacy -> Microphone window.
I've tried the workarounds listed on the Firestorm Mac help page in Firestorm and Alchemy which involve running the package from terminal, creating an audio device, and reinstalling to no avail. There are posts for other apps, such as this one for League of Legends, which recommends disabling the system integrity check and making changes to the sqlite system database... no thanks.
As Gavin said, this is how it is going forward. I'm happy to help test, contribute to a bounty, or attempt compiling and signing viewers myself under my Apple developer account with someone's help to get this resolved as soon as possible.