Gmail connector omits Inbox messages classified as "suspected spam" (delivered via Workspace admin override)

Environment: Claude Code + the managed Gmail connector (gmailmcp.googleapis.com), Google Workspace account.

Summary: The Gmail connector's search_threads (and therefore get_thread) cannot return a message that is present in the user's Inbox when Gmail has classified it as suspected spam but a Workspace admin policy force-delivered it to the Inbox (Gmail shows the banner "This message wasn't sent to spam due to your organization's email settings"). The message is invisible even with in:anywhere and includeTrash: true.

Repro:

1. An Inbox message from an automated sender (e.g. a ticketing/Atlassian notification) that Gmail flagged as suspected spam but an org policy allow-listed into the Inbox — shows the External tag plus the org-override banner.
2. Call search_threads with each of: from:<sender>, subject:<word-in-subject>, after:<date> "<word>", "<unique-token>", and in:anywhere subject:<word> with includeTrash: true. All return nothing (or only unrelated / Sent items).
3. Other inbound mail to the same address received later the same day IS returned — so this is not indexing lag and not a wrong-account issue.

Impact: Automated mail that organizations routinely allow-list past spam (ticketing systems, ops/security alerts) is silently invisible to Claude, with no error surfaced. The user has no signal that the connector is omitting data — they reasonably conclude "the email isn't there."

Expected: Messages present in the Inbox should be searchable/returnable regardless of spam classification; at minimum in:anywhere (and includeTrash: true) should include them.

Likely cause: The connector appears to apply a spam-exclusion filter keyed on the message's classification rather than its folder/label.