I solved the problem in Gitlab.com 16.2 via allowing access to my second project CI_JOB_TOKEN
this can be done in your base project in Settings > CI/CD > Token Access
you will need to add full notion of you “client” project, i.e. GROUP/SUBGROUP/PROJECT_NAME
after that in client project use docker login via token
docker login -u $CI_REGISTRY_USER -p $CI_JOB_TOKEN $CI_REGISTRY