I found the issue: There needs to be a codecov.yml in the repo root. That is even though -y ci/codecov.appveyor.yml is used which should make this work without one. Hence there seems to be a bug with the server-side handling of that yaml file. Intrestingly this does not apply to the travis environment where it works perfectly fine without any yaml at all.
I guess that this is due to Codecov cannot analyze Cobertura reports from AppVeyor which requires an entry in the yaml file to accept the reports