Standarize dictionary keys for storing user groups/teams/organizations in auth state?

[consideRatio]

Extracted from https://github.com/jupyterhub/oauthenticator/pull/594 and https://github.com/jupyterhub/oauthenticator/pull/594#discussion_r1209744293.

• open issue about standardizing a flag like populate_teams_in_auth_state in all authenticators and the naming for the teams key, holding the info about the teams the user is a member of. (Eg. in bitbucket.py the key is called user_teams and we set it by default without any flag, but in github.py we have a flag and call it teams). Consider allowed_orgs too as for standadization.

[consideRatio]

I see the value of standarizing this mainly stems from that the logic in this project can be simplified, but I value not doing it because it would be a breaking change.

I'm currently weighing pro/con's to think that this isn't worth pursuing, at least not for the next major release (oauthenticator 16).

[minrk]

I'm currently weighing pro/con's to think that this isn't worth pursuing, at least not for the next major release (oauthenticator 16).

If it helps simplify things, we can go ahead. The breaking change can be avoided by populating both fields for a time and deprecating the old field, if that is helpful.