I have been in touch with the company I purchased the mic from. My most recent communication from them was as follows: Hello,
"I just want to keep you updated on the current status of this case. I have continually checked up with AKG on this one and their team is still looking into compatibility with OS 11.4. To my understanding, it seems that some users are experiencing this and other are not so it still unclear.
It seems that conducting the resets that apple had you try has helped some users. It was recommended that you try a few times as some experienced a solution but after more than one reset. For your convince, you can reference these articles should you choose to try the resets:
Reset NVRAM or PRAM on your Mac - Apple Support
How to reset the SMC of your Mac - Apple Support
I will keep you in contact with any further updates."
AKG's service department sent me the following:
"I had another tech try it out on a Mac system with Big Sur. He had tested it in Ableton initially, but it did not work. He then installed Audacity (another DAW which is free) and it prompted him for microphone permissions. It worked in Audacity, and then it showed in the Mac Security and privacy section for mic permissions. He was then able to check it for Ableton, and then it worked in Ableton.
So you could try installing Audacity and see if it prompts you for permissions or shows it in the mic permissions settings of the Mac."
Neither of these solutions worked for me, but I post them in the hopes that they will help someone.