Why is Audacity 2.3.X not recording audio input on macOS Catalina, plus workaround
There is a work-around for this, and I wanted to share it here as yet another avenue to seeking this information.

1) Go to Applications > Utilities

2) Launch Terminal.app

3) in the Terminal dialog type the following command following command:
open /Applications/Audacity.app/Contents/MacOS/Audacity

This will open Audacity and then Terminal will actually ask for the correct permissions.

this assume that Audacity is stored in your Applications folder. If it is somewhere else, you will need to change the path in the above command:
open /*location of audacity*/Audacity.app/Contents/MacOS/Audacity

Since microphone access permissions granted in Mojave do not pass through to Catalina. Once you have granted this access in Catalina you should not be asked for it again when relaunching Audacity with this workaround method.