Updating microG from F-droid probably will not install because the signatures will not match, so blacklist it in F-droid and wait for /e/ to update it. Unless you changed the settings /e/ App updates will install automatically and the notification will remain to let you know about the update.
In the screen shot on your first post you can see the three dots at the top right. Select that and then select “ignore all updates”. Sorry I remembered wrong, “blacklist” is used with Aurora Store and not F-droid. The e Apps update notification tells you “App updates will be installed automatically”. The update has already been installed. There is no hidden update! MicroG is part of the ROM or operating system and will probably be updated with the next build for your phone.
I just recently turned Automatically install updates back on. Before it was on I would regularly get told that I have updates available (e.g. 4 app updates available) but when I went to look there would always be 1 less app appearing under Updates (3 app updates) And when there’s 1 app update available nothing appears under Updates.
Turning back on Automatic updates seems to have changed nothing as the mystery app never appears and I can’t ever seem to find out what it is.
I have not had that problem with e Apps. My only idea is close all the apps that are running in the back ground, clear the storage for e Apps in system setting and reboot the phone. That may fix the update count problem.