Introspection of the OData schema (e.g to convert to GraphQL) reveals the Manager's metadata to be insufficiently typed and not declaring any user properties.
Manually tending to the metadata before usage allows to workaround this:
Replace <NavigationProperty Name="manager" Type="graph.directoryObject"/> with <NavigationProperty Name="manager" Type="graph.user"/> in the data from https://graph.microsoft.com/v1.0/$metadata - then the me/manager query also returns user attributes for the manager of the queried user.
Refs MS Uservoice: https://microsoftgraph.uservoice.com/forums/920506-microsoft-graph-feature-requests/suggestions/37700059-add-manager-to-list-users-graph-api
Would you consider this a bug? Can I expect it to get fixed soon?