When you “Open” - the latest Apple instructions say to use Finder on the Applications folder (assuming you dragged it in there in install) and then Ctrl-click it and select “Open” from the Menu. Double or single click on the app will not work now until after this has been done.
Another thing to check if that fails, is whether you can open XQuartz (and then go to its menu and open it’s terminal). After installing XQuartz for the first time you have to logout/login (or reboot) in order to get the Display set up for it. And XQuartz needs to be re-installed after a OSX version upgrade, of course - otherwise its settings will not be good.
From your description, the first idea seems most likely as the issue to me. I remember the time it took me to discover this approach when Catalina was introduced - and Apple has now back-migrated this to Sierra onwards. They are afraid of downloaded nasties, of course, and users simply “clicking through” after download. We can’t meet the requirements to get into Apple’s signing program - (not a legal entity registered as a company or an individual who is able to make that happen - with enough gold). Microsoft is doing similar things, (total = gold*2) so unfortunately it is our users who have to find their way around the usability blocks.