Self-Hosted Main

From what I understand, those services would allow to only allow Traefik to redirect the user to the appropriate service if correctly authenticated, is that correct?

Exactly. In Traefik, this is often called a forwardAuth middleware. Only if you are authenticated against Authelia/Authentik, Traefik will obtain the go to proxy the user request to the actual proxy service.

Also, using either Authentik or Authelia, user can use SSO to register/login ? How can I control who can register?

Yes but it depends on the proxied application. Some do not support OAuth/OIDC/SAML and whatever. Then, you have to authenticate against Authelia/Authentik and a second time at the service via username and password usually. Some apps however support it. Then you can setup the app and Authelia/Authentik for SSO. If done, only a single login against Authelia/Authentik is required and you'll be automatically logged into the app. No second login necessary. Authelia/Authentik will handle it. Whether a user can register or not depends on the app and how it is setup. Portainer e.g. can allow SSO user registering but also deny it. If denied, you'd have to create the users first manually in Portainer with the same email address as in Authentik. Then the user can login.

For instance I use immich to backup my pictures, so in the immich mobile app server settings I have : immich.mydomain.com, how would that works out if I use either Authentik or Authelia?

Unfortunately, Immich does not support OAuth/OIDC/SAML yet. Therefore, you are left with authenticating against Authelia/Authentik and then as well against immich via your user credentials. As correctly assumed, this requires a web browser to obtain the Authelia/Authentik login screen. For the immich mobile app, this is not possible.

There is some discussion on GitHub here about this topic:

https://github.com/immich-app/immich/discussions/3118

I've also implemented Authentik with Traefik. May read here:

https://blog.lrvt.de/authentik-traefik-azure-ad/