Rebuilt from PR #61283 onto the /p/<profile>/ routing world (7aa21e336):
_profile_scope(None) now enters the DEFAULT profile's runtime scope when
multiplexing is active instead of returning nullcontext(). api_server is
a port-binding platform living on the default profile, so plain requests
(no /p/ prefix) are the primary path — with fail-closed get_secret they
crashed with UnscopedSecretError on the first credential read (#61276).
All three wrapped call sites (chat-completions executor, /v1/runs agent
construction and _run_sync) inherit the fix through the one seam.
Single-profile gateways keep the no-op. Regression tests ported from
the original PR to the _profile_scope seam.
Fixes#61276