AC blows warm

The Ac on my 2018 A6 started blowing warm air very out of the blue. No issues prior. Everywhere around me is booked for weeks. I can’t even do a quick refrigerant check to see if it needs Freon. I however was able to get an app at dealership scheduled for next fri. I added a vid where I have the ac and fan on and to me it seems the compressor is not even engaging(pls correct me if I’m wrong) any idea what the culprit might be. A week is too long for me to not know what’s wrong lol. Thanks in advance.