FirebaseAdminError: This version of the Admin SDK requires Node.js 14 or later when deploying to Cloud Functions 1st gen

Compatibility conflict between Admin SDK v11+ and Cloud Functions 1st gen runtime

Deploying a Cloud Function that depends on Firebase Admin SDK v11.0.0 or later to a 1st gen Node.js 12 runtime fails at initialization with the error FirebaseAdminError: This version of the Admin SDK requires Node.js 14 or later. The 1st gen Node.js 12 runtime reached end-of-life in March 2023 and new deployments are blocked, yet migrating to 2nd gen (Node.js 16/18/20) requires refactoring trigger definitions (Eventarc instead of functions.https.onRequest) and adjusting for different cold-start behavior.

Pinning the Admin SDK to v10.x avoids the Node.js version error but limits the project to critical security fixes only; v11+ also introduces breaking TypeScript changes in Auth, Firestore, and Messaging APIs that may block upgrades even after the runtime is satisfied. No automated tool validates the Admin SDK + Functions runtime + Node.js version triplet at deploy time.

Questions

1. What is the recommended migration path for a 1st gen function using Admin SDK v10.x that must move to a supported runtime without a full 2nd gen rewrite?
2. Can the Functions emulator reliably surface Admin SDK version mismatches before deploying to 2nd gen Node.js 18/20?
3. Is there a documented compatibility matrix that maps Admin SDK minor versions to Cloud Functions runtime versions and Node.js engine requirements?