chore: upgrade Firebase Functions to Node.js 22 and firebase-functions v7

Node.js 20 is being decommissioned 2026-10-30. This upgrades the runtime
to Node.js 22 (LTS), bumps firebase-functions from v6 to v7, removes the
deprecated functions.config() fallback, and aligns the TS target to ES2022.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

backend/package.json

@@ -53,7 +53,7 @@
     "express": "^4.18.2",
     "express-rate-limit": "^7.1.5",
     "firebase-admin": "^13.4.0",
-    "firebase-functions": "^6.4.0",
+    "firebase-functions": "^7.0.5",
     "helmet": "^7.1.0",
     "joi": "^17.11.0",
     "jsonwebtoken": "^9.0.2",