With one of the templates, I have identified the issue is a single Template Variable.
The TV is a resource list.
Working on the other Templates to determine if the issue is other TVs.
I wonder what possibly caused the issue with the TV, was it the upgrade, DB issue, or a problem with modx.
It could be a mod_security issue. That's the most common cause when specific things can't be saved. The first thing to try, though, is using private or incognito mode in your browser, in case it's a leftover cache file or cookie from the earlier MODX version.
I was able to fix the issue. I switched the TV to content type text. Test opening the resources for editing, worked fine. Then I switched back to content type resource and all worked as expected.
Not sure why the issue arose. It might have had something to do with the upgrading modx from 2.6.5 to 2.7.0.