[northersubair]

feat(search): add global search API and header search UI

Summary

Backend

• New SearchModule / SearchService / SearchController exposing
  GET /api/v1/search?q=<term>, registered in AppModule.
• Searches:
  • Courses — title and description, published only.
  • Lessons — title, published only, with the parent course title and
    courseId for navigation; the parent course must also be published.
  • Currencies — name and symbol.
• Returns at most five results per group, ordered by title/name.
• Uses LOWER(column) LIKE :term rather than PostgreSQL ILIKE so the same
  query works against the SQLite database used in development and CI.
• Public endpoint with @Throttle({ default: { limit: 30, ttl: 60_000 } }).
• SearchQueryDto requires a 1–100 character string and is documented in
  Swagger.

Frontend

• New components/search/global-search.tsx: header search icon that opens an
  input, debounces requests by 400 ms, aborts in-flight requests when the query
  changes, and handles Escape, click-outside, loading, error, empty and
  minimum-length states.
• Results are grouped into Courses, Lessons and Currencies, and each row
  navigates to /courses/:id, /courses/:courseId/lessons/:lessonId or
  /currencies/:id respectively.
• Added to the header in both desktop and mobile layouts.

Testing

• npx jest src/search --runInBand — 2 passed (blank query short-circuit and
  grouped mapping/limit).
• npm run lint (backend) — 0 errors (pre-existing warnings only).
• npm run build (backend) — succeeds.
• npx eslint components/search/global-search.tsx components/header.tsx
  (frontend) — passes.
• npx tsc --noEmit (frontend) — only the pre-existing
  app/profile/page.tsx parse error remains; no errors in the new files.

Closes #286