Hello,
I have performed the steps you suggest, including from Chrome which I had not yet installed on my system.
I have been able to obtain the appropriate free license and registered my computer with the self service.
Then I tried to get Questa going, going by the license message the program shows when starting up. This means I went to a command prompt, set the environment variabele LM_LICENSE_FILE and pointed it to the location I placed the generated license. This made Questa work when starting from that command prompt. After this, I made a batch file to start Questa from.
However, I don't think this is a permanent solution. I noted that there is no license service installed on my systen. Nor did previous versions for both Quartus and Modelsim ask for license files where they just ran after starting them.
Might it be possible that somehow the download for Questa itself was the download for the Standard edition download section? Because you see, I attempted to download Quartus two times from the supported devices list. And when the installer started, its title showed that the Standard version was being installed. So I canceled that and just removed the files again. In the download panel it was visible that I clicked the right download link - the downloaded file itself had "lite" in the filename.