feat(web): restore header search icon on non-home pages

[mrviduus]

Summary

User-reported regression: search is no longer discoverable on inner pages.

"пожалуйста добавить иконку поиска и поиск в хедер я знаю мы его удаляли но по моему он нам нужен потому что сейчас не очевидно где его искать"

Search icon was removed in 3e53e3e ("clean header") on the assumption that the hero search input on home was enough. It wasn't — on every other page (library, discover, vocabulary, reader, book detail, …) the hero is gone and users have no entry point to search.

Changes

• Header.tsx — re-import MobileSearchOverlay, add useLocation + isHomePage regex (/^\/(en|uk)?\/?$/ — covers /, /en, /en/, /uk, /uk/), render search icon button only when !isHomePage. Clicking opens the overlay (was orphaned in Search.tsx, now wired back up). Wired to existing emit('header.click', { item: 'search' }) telemetry channel.
• en.json — nav.search i18n key.
• Header.test.tsx — +10 cases:
  • icon hidden on /, /en, /en/, /uk (home variants)
  • icon visible on /en/library, /en/discover, /en/vocabulary, /en/books/foo (inner pages)
  • clicking icon opens overlay
  • overlay close button removes it

Why keep home iconless

Home's HeroSection renders a prominent full-width search input. Putting a second search icon in the header would be visual duplication and pull attention away from the hero. On every other route the hero is gone — that's where we need the chrome affordance.

Tests

• pnpm test — 484 passed (was 474, +10 new Header cases)
• pnpm tsc --noEmit — clean
• Manual Playwright snapshot:
  • /en/ header: Upload + dark_mode + Sign in (no search icon ✓)
  • /en/books/ header: Upload + Search + dark_mode + Sign in (search icon present ✓)

Rollback plan

Single revert — git revert <merge-sha>. No DB / API / behaviour changes. Pure UI restore.

Notes

• MobileSearchOverlay was already maintained in Search.tsx (used by HeroSection). This PR just adds a second call-site; no new component code.
• The isHomePage regex matches both /en and /uk roots — if a third locale lands, extend the alternation.
• Telemetry event header.click already exists; new item: 'search' value will start showing up in dashboards immediately after merge.

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