Soft-delete a project.

Requires ADMIN role in the project's workspace (the write service decides). The project drops out of every list and read and its access keys stop authenticating; its data stays for the retention window.

Args: request (Request): Incoming request (rate-limit plumbing). response (Response): Outgoing response (rate-limit plumbing). auth (AccountStampedAuth): Account-scope user auth (session token or CLI access JWT); its resolved user_id becomes the actor. project_id (str): The project to delete. reason (str): Why it is being deleted; recorded on the audit row. _live (None): Write-path liveness gate (blocks a revoked JWT session).

Returns: DeleteProjectResponse: The removed project.

Raises: HTTPException: The write service's 400/403/404 verbatim, or a 503 when its response is ambiguous.