[BACKEND] Add a health check that reports storage mode and DB connectivity

[Trovic1]

Summary

Extend the health route to report whether storage is postgres or local-json and, for Postgres, whether a test query succeeds.

Scope

• backend only

Likely files

• src/app.js
• src/lib/db.js

Acceptance criteria

• Health returns storage mode
• In Postgres mode it reports DB reachable/unreachable without leaking credentials
• Returns 200 when healthy, 503 when DB is required but down

Verification

• Run with and without DATABASE_URL and confirm the reported mode

Labels: backend, enhancement, good first issue

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[harshaggarwal101]

Hi! I'd like to work on this issue if it's still available. Could it be assigned to me?