I had the same problem with Questa.
For the current poster it now probably works because now there has been given a "Guaranteed-to-work reality" through the effort of the Intel support engineer.
In my case, I had the same command shell popping up and out without a Questa starting up. I went through the same of obtaining a license through the licensing self-center to no avail.
Then, I thought, let's be clever and pull out an old fashioned DOS trick (no not the cyber attack; the disk operating system instead). And made a batch file that set the environment variable and would then start the Questa executable. This miraculously worked!
For reasons, I later ununstalled that version of Quartus and Questa and went back to version 20.1.1 for both, then called ModelSim.
Yet again later, I installed the latest again. Including the latest of Questa. No luck running Questa, same deal with the command shell. Then I thought, let's create the batch file again since that was a workable solution. Only to find out this trick no longer worked for me, no matter what I did. Given my prior experience and given this topic, it looks and feels like there is some sort of "progressive learning" at work.
Whenever I decide to install Questa again, I may request support to have this "guaranteed-to-work reality" through supplying system name and MAC to Intel.