So I am always hesitant to upgrade my MacOS when everything is working well. I made the mistake of upgrading from Catalina to Monterey a couple of days ago. Now experiencing problems with Elements 2021. The first time I ran it no probem. Opened an image, edited it and save it. A few hours later I try to open another image and Elements hangs up and I need to force quit. Chatted with support and was surprised to find out that I need to purchase Elements 2022 (something about legacy issues). Support agent didn't really seem to care. I have had previous versions of Elements that worked fine through many of the "Mountain" OS upgrades. The odd thing is if I delete Elements, re-download and install it again will work once and then not again. There has to be a fix for this other than purchasing Elements 2022. Very frustrated with Adobe.
I know very little about Macs but it is my understanding that Elements 2021 will work OK if you have Monterey version 12.1 or later installed.
I'm curious whether you are as frustrated with Apple as you are with Adobe. An OS is supposed to allow other applications to run. When originally released, Apple failed to ensure that any version of Elements ran properly. It subsequently issued a new release that allowed Adobe to create a fix for Elements 2022 and supposedly allowed Elements 2021 to work. It has not done so for earlier versions of Elements and, at least according to your report, has not done so for Elements 2021.
I upgraded to Monterey 12.2.1 from 12.1 just a week ago. I think I'm frustrated with both. I have sent multiple error reports to Apple so I will see what happens over the next few weeks. For now I have just uninstalled it again. I long for the "old days" when updates were provided for applications and the OS and they worked. I think part of the issue is that OS's are getting so complex. My old version of Elements 13 worked fine though all of the "mountain OS's". You would think Elements 2021 would continue to run in 2022!
Adobe apparently has no interest in support older (legacy) versions of their products. Affinity Photo is a fantastic replacement with great customer support.