In Chrome on a MacBook Pro running OS Big Sur 11.4. It's been more than 12 hours since I could log in. I can enter my password but The site just spins and says Reconnecting... For hours.
if I open on several tabs for some reason I can open a menu page or get to the page where I can select a bots game, but then it just says I need to be logged in (even though the menu on the left says "log out")
This sounds like the "Spinning Castle problem":
In order to get out of the Spinning Castle problem, you need to open a private(Firefox) or incognito (Chrome) window , go to dominion.games, enter your Name and Password, but don't click "Login". Instead, click on "Kick and Resign" (rightmost button below the login area). Then you should be able to login normally (no need for private/incognito tab).