I have read about the compatability issues of Elements 20 and Monterey. However, it opened & worked yesterday. There were no computer updates since then. Today I just keep getting the Adobe sign in screens over & over, even though it accepts my info as correct. Is this a sign in issue? When I sign into my Adobe account, it does not show any active devices (the old or new Mac) & I do not get the "Manage Plans" option, although it shows the current version version of elements under "Your Product." Of course, Elements still works on old Mac, but I don't understand why it worked yesterday & not today.
Try contacting Elements support. You can start a chat session by clicking on the blue Contact Us button under the Help & Support menu at Adobe.com. Or you can contact Support by telephone using the numbers listed here: https://helpx.adobe.com/contact/phone.html.