Add persistent WebSocket backend deployment support

[saurabhhhcodes]

Summary

• fix production backend startup so persistent hosts like Render/Railway/Fly.io/Docker call server.listen() while Vercel serverless still exports the Express app
• add /api/health for deployment health checks and runtime metadata
• add tested runtime helpers for Vercel detection and port parsing
• add a backend Dockerfile, Render blueprint, deployment guide, and updated environment documentation

Fixes #74

Testing

• /Users/saurabhkumarbajpaiai/.cache/codex-runtimes/codex-primary-runtime/dependencies/node/bin/node --test tests/*.test.js ✅ 3 passed
• /Users/saurabhkumarbajpaiai/.cache/codex-runtimes/codex-primary-runtime/dependencies/node/bin/node --check server.js ✅
• /Users/saurabhkumarbajpaiai/.cache/codex-runtimes/codex-primary-runtime/dependencies/node/bin/node --check lib/runtime.js ✅
• git diff --check ✅

Note: npm is not installed in my local shell, so I ran the package test entry directly with the bundled Node runtime.

GSSoC labels

The issue already has gssoc:approved, level:advanced, and type:performance. After review, could you please keep/add the matching PR labels and any quality label you think fits?

[vercel]

Someone is attempting to deploy a commit to the Sameer's projects Team on Vercel.

A member of the Team first needs to authorize it.

[ThePlator]

Hi @saurabhhhcodes! Thank you for the incredible effort on this PR—it is extremely thorough and well-documented.

As noted in Issue #74, we had previously assigned this task to @roshankumar0036singh to give him the opportunity to implement his suggestion. However, to keep the project moving forward, we have set a deadline. If Roshan does not respond or provide an update by tomorrow afternoon, we will go ahead and merge your PR.

Thank you for your patience and for such a high-quality contribution!

[saurabhhhcodes]

Thank you for the update and for being fair about the original assignment. I completely understand giving @roshankumar0036singh the deadline first.

I’ll keep this branch ready and won’t make unnecessary changes unless you ask for something specific. If you decide to merge it tomorrow, please also keep/add the scoring labels from the issue (gssoc:approved, level:advanced, type:performance, and any quality label you think fits).

[saurabhhhcodes]

Updated this branch with the latest main and resolved the merge conflicts.

What changed in the conflict resolution:

• kept upstream's newer Docker/Render deployment setup and health-check wiring
• preserved the runtime helpers/tests from this PR so persistent hosts still call server.listen() while Vercel serverless exports the app
• verified the branch is mergeable again on GitHub

Validation after resolving conflicts:

• node --check backend/server.js ✅
• node --check backend/lib/runtime.js ✅
• cd backend && node --test tests/*.test.js ✅ 3 passed
• git diff --check ✅

Please add gssoc:approved, an appropriate difficulty label, and type:devops/type:feature if this is ready to count for GSSoC.

[saurabhhhcodes]

Refreshed this branch on latest main and resolved the conflicts.

What changed in the refresh:

• kept upstream's newer chat/problem/challenge/socket work intact
• preserved this PR's deployment documentation and runtime-helper refinements
• kept the PR diff focused to deployment docs plus runtime helper behavior

Validation:

• node --check backend/server.js
• node --check backend/lib/runtime.js
• npm --prefix backend exec vitest run tests/runtime.test.js (10 passed)
• git diff --check

The branch should be mergeable again; the remaining red status, if any, is expected Vercel authorization.