API: User mtime property for checking any modification

I notice mtime is in many parts of the user but clients might prefer a single mtime which covers if the user object changed in any way (so we can update local copies). (Also you could use that to 304 not modified on a user resource request.)

For example, basics.mtime is only modified if basics change (profile.mtime on profile change). If would be nice to have a mtime in the root which covers any modification.

Currently I'd have to check basics.mtime, basics.last_id_change, profile.mtime and maybe others?

The issue names no files, tests, or entry points, so first locate the user API resource and identify every user subcomponent that can change. Confirm the intended root-level mtime semantics, including whether it supports conditional 304 responses, then document the affected API behavior and add coverage for changes to each relevant component.

Written by the indexing model from the issue text.