When trying to add the Github Registry to Synology Docker, I always get a prompt saying "Registry returned bad result".
The URL I try to connect to is: https://ghcr.io
I'm trying to do the same (DS920+, DSM 7.1 latest). According to this Reddit:
https://www.reddit.com/r/portainer/comments/u1vf1s/how_to_add_ghcr_as_a_registry/
it used to work with 'docker.pkg.github.com' as the repo url, but according to the current Github docs, it was the old namespace and the actual repo is now 'https://ghcr.io'
According to the docs, authentication is implied many times, maybe it is not possible to use the repo w/o authentication (tried with access tokens, not working).
I opened a Synology support ticket, let's see what they can say.
2022-10-27 - Synology Support replied and the official statement is that the token authentication currently used by Github Container Registry is not supported on the DSM's Docker package GUI. Its possible to ssh to the DSM and use docker from the command line.