Whatever the reason was, it seems to be gone now. With quarkus 3.20.4 and quarkus-rest I can use my services as expected.
The required backend systems to start the affected system are no longer available, so I can’t verify whether it was due to the quarkus version or other reasons.
Bottom line: a small test project with the same method signature does work as expected with quarkus-rest instead of resteasy(classic) and also the current version of our application seems to work fine with quarkus-rest.