feat: add AI chatbot integration and update UI components

[Utkarsh28022007]

What changed

Added AI chatbot integration, updated NavPills component, updated Yaksha2026 program page, and cleaned up deprecated HomePage.

Related issue

Type of change

• Bug fix
• Feature
• Refactor (no behaviour change)
• Docs / comments only
• CI / tooling

Area affected

• Backend (Express / Mongoose)
• Frontend (React / Vite)
• Admin / Train tab (/admin/*)
• Community (/community — posts, comments, auto-answer)
• Search (hybrid text retrieval, training stats)
• Auth / middleware / samagama.in bridge
• Crons / schedulers / embedding-warm
• Observability (Sentry / logging / Discord alerts)
• Docs

CI verification

• cd apps/backend && npx tsc --noEmit exits 0
• cd apps/backend && npx vitest run — all tests pass
• cd apps/frontend && npx tsc --noEmit exits 0
• cd apps/frontend && npx vitest run — all tests pass
• pnpm run lint — 0 errors (152 warnings is the baseline)
• GitHub Actions green on the merge commit (CI, CodeQL, Build & Deploy)
• Tested with a real API hit or browser interaction if behaviour changed
• Tests added or updated for the change
• Single logical change — unrelated fixes noted in description, not fixed here
• Docs updated if route / API / env var / pipeline behaviour changed
• Rebased onto main, no merge commits

Notes for reviewer

[Kritika-1301]

Reviewed the changes

[Kritika-1301]

The AI chatbot integration looks good.
Yaksha2026 page updates are clean