**Description** <!--What needs to be improved? What should be done? Has there been any related work before? Any relevant links or material? --> Context: https://github.com/sigstore/scaffolding/tree/main/actions/setup-sigstore-env The fakeoidc container was reimplemented in this setup as well. We can greatly simplify the [end-to-end testing bash script](https://github.com/sigstore/cosign/blob/main/test/e2e_test.sh) by leveraging the [run-containers script](https://github.com/sigstore/scaffolding/blob/main/actions/setup-sigstore-env/run-containers.sh). Previous impl: https://github.com/sigstore/cosign/pull/4161