feat(gateway): dual-mount legacy routers on /api and /api/v1 (Stage 1 PR5)

Strip /api prefix from 13 legacy router APIRouter() declarations and dual-mount
each on prefix="/api" (backward compat) and prefix="/api/v1" (versioned surface)
in app.py. Auth, service-accounts, api-keys, assistants-compat remain single-mount.
Update 10 test files to pass prefix="/api" when directly including stripped routers.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

backend/tests/test_runs_api_endpoints.py

@@ -17,7 +17,7 @@ from app.gateway.routers import runs
 def _make_app(run_store=None, event_store=None, feedback_repo=None):
     """Build a test FastAPI app with stub auth and mocked state."""
     app = make_authed_test_app()
-    app.include_router(runs.router)
+    app.include_router(runs.router, prefix="/api")
 
     if run_store is not None:
         app.state.run_store = run_store