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_threads_post_workspace.py

@@ -37,7 +37,7 @@ def _build_app(workspace_id: str):
     app.state.store = store
     app.state.checkpointer = checkpointer
     app.state.thread_store = MemoryThreadMetaStore(store)
-    app.include_router(threads.router)
+    app.include_router(threads.router, prefix="/api")
     return app, store