We do have a solution for this. It's a bit of a process, but it shouldn't be too technical and we will look to implement its setup in our own installers sometime in the near future.
The problem is that Soundflower is no longer able to be installed in Big Sur as it is not supported by the developer (we are not the developer).
An alternate open-source process called BlackHole can be used in its place to enable audio recording. For now it needs to be installed and configured manually.
BlackHole installation and setup:
If making several recordings in a row then repeat Steps 9-10 as many times as needed before finishing (Step 11).
This manual configuration and recording process (minus Steps 3 and 4) will need to be repeated each time the application is opened to start a recording.
Also, if you are wanting to use the Audio Capture mode in Jaksta Music Recorder then similar steps will need to be taken. Let me know if you need any guidance with that if you can't work it out easily enough.
I have followed the above procedure (several times) but I am not hearing the audio during recording and there is no audio when I play the recording back.
I have followed the procedure (several times) but there is no audio through the speakers during screen recording and there is no audio on the recording.