ChromEdge ("MSEdge for Windows 7") has its own updater.
Switching off Windows Update would not help.

Microsoft Edge Elevation Service = elevation_service.exe
Microsoft Edge Update Service (edgeupdate) = microsoftedgeupdate.exe
Microsoft Edge Update Service (edgeupdatem) = microsoftedgeupdate.exe

Using Sysinternals Autoruns, the Chrome mechanism is:

Google Chrome Elevation Service = elevation_service.exe
Google Chrome Update Service (gupdate) = googleupdate.exe
Google Chrome Update Service (gupdatem) = googleupdate.exe

Many of the mechanisms used by the two, are the same.
One difference is, in Programs and Features, Google Update
is no longer visible as an uninstallable feature. I think
a few years back, it may have had a separate entry.

These do not exactly rely on Windows Update, either of them.

The googleupdate service, was supposed to have the logic, that
it would only "remove itself" if all Google products were
uninstalled. I was unable to get it to do that (remove itself).
By not having a Programs and Features entry, this is intended
to make it (almost) impossible to remove. by the usual naive means.

Paul