SO while waiting for the towing, I was able to replace the Key fob battery. It didn't work right away but I went back inside my house and returned after 45 minutes and everything was fine again.
So the THEORY is right! the only other possible issue is that the Electrical System Error is not...
I'm having the same problem on my Taycan Turbo 2020. Yesterday it started after few minutes but this morning I'm having the same problem permanently. Just called for towing.