Thanks, @hmerk. That was finally it. I changed the version number of my binding from 1.0.0-SNAPSHOT to 2.0.0-SNAPSHOT and now it works fine in an OH2 karaf container.
Actually, so far I tested against an ESH workspace and started everything from a run configuration.
Still, I do not understand, why from an OSGi perspective, the start of the bundle should fail just due to a low version number. OH2 could not have any explicit dependency to my bundle… Is that some karaf property?