Thank you for the thorough answer. I wound up opening solitaire and letting it run. It took waaaaay longer for the quest to pop than I was giving it.
Not actually true I don't think. I've gotten the quest multiple times with Marvel Puzzle Quest on Steam. Live might make it pop sooner but it isn't required.
Just for reference, I started Battlefield 2042 on EA desktop via Game Pass at 12:01 AM PST and stopped at 12:08 AM. I started Cyberpunk 2077 on Steam right after and stopped at 12:15 AM. It's been 20 minutes and nothing has popped up.
When I played Nobody Saves the World yesterday for about a minute to pop an achievement, the quest completed about 8 minutes after I popped the achievement. So let's say it should take about 9-10 minutes to show up after you start a game.
EDIT: Still nothing as of 1:01 AM. SAD!
EDIT 2: Started up Windjammers 2 for the first time at 1:21 AM, got to the menu and then quit. Quest popped at 1:27 AM, 6 minutes after.