Audacity has stated that they do not support macOS Catalina, 10.15.X. Given the permissions and app sandboxing schemes have changed for the latest version of macOS, simply starting Audacity will not prompt users for granting the permissions it needs to use the built-in audio device or other audio input devices. So even though you can start recording, the software will never receive any input. You'll notice this looking at the waveform visualization during your recording.
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:
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.