Good news:
The latest release of the CCTG app (1.9.1.6) has a fix for the problem. According to the ChangeLog:
Fix microG version check on /e/ ROMs (/e/ has two possible microG versions, one with ENF and one without. The one without ENF will now be correctly ignored.)
I updated the app via F-Droid and can now confirm that
- The app starts normally without reporting insufficient support in microG AND
- Gathering IDs apparently did continue also while running the incompatible version (as correctly presumed by @DarthDavester).
Problem solved for me. Thanks to all for this quick solution!