tl;dr: my fault, fixed in next release.
Longer story. GAM has historically requested a special "email" OAuth scope. This scope allows GAM to ask Google's servers which Google email account the admin used to authorize GAM. These parameters were returned in Google server responses as part of an ID Token's email and hd (hosted domain) parameters.
Fast forward to earlier this year, GAM uses a LOT of OAuth scopes. Google Classroom alone has 5 scopes, the Admin SDK APIs have one scope per each of users, groups, domains, orgunits, user schemas, etc, etc. All this means GAM has started bumping up again Google's limit of 30 total scopes. So Ross and I have been looking for ways to reduce the number of scopes GAM uses so there's plenty of room for new scopes as Google releases new APIs.
Around this time, I replaced the old "email" scope with the "profile" scope. I'd found that the profile scope still allowed retrieval of the authenticated admin's email address (even though that wasn't documented). And while the email scope mapped to two real scopes and used two of the thirty scopes, profile only mapped to one so it was a saving of one scope.
So it looks like Friday, this was changed so that the profile scope could no longer get the authenticated user's email address (as I said before, the fact that it ever worked was undocumented so not the best decision on my part to switch).
So the next GAM release after 4.12 will go back to the email scope. I've managed to reduce GAM scopes somewhat in other ways by switching GAM to always use service account authentication for things like sending email, saving a report to Google Drive and modifying Google Calendar ACLs so we should still have room for the next APIs.
For now use Ross's GAM_DOMAIN environment variable workaround but this should be resolved in the next release.
Jay