Though we're missing a CRUD interface for individual associations, the whole list of config groups can be set via config_group_ids and config_group_names attributes on both host and host groups.

It seems it's not documented https://github.com/theforeman/foreman/blob/develop/app/controllers/api/v2/hosts_controller.rb#L40

Yeah, they're almost entirely missing. A few have been added over time where somebody has wanted it documented, but we've not done it wholesale.

#2945 added these magic attrs originally and #2931 put it into API responses consistently, but from what I remember of the discussions at the time, Joseph wanted to find a way to document it automatically, which hasn't happened. We've established a pretty comprehensive list in #7568 which could be copied to API docs.