I’ve figured it out myself. The issue with the “missing gradle project configuration file” arises from the way the gradle project(s) are imported into Eclipse.
When importing a gradle project via the regular File -> Import -> General -> Existing Project into Workspace command, then it will not work and produce the aforementioned error.
However, if you import the very same project via File -> Import -> Gradle -> Existing Gradle Project, then you get a different import wizard, and with this wizard, it works like a charm.
I still think it’s a bug because the choice of the import wizard should not matter. Still, choosing the proper wizard is a viable workaround.