feat(landing): add guest landing page

[DIvanCode]

Summary

• add the public guest landing at / while preserving the existing authenticated HomePage
• present the duel as optimized light/dark preview images, with a compact layout sized close to the previous 75% browser-zoom appearance
• allow the landing content to scroll vertically on short screens and keep the mobile layout free of horizontal overflow
• route the CTA to reload-safe /auth?tab=register, hide the redundant Header Войти action on /auth, and keep a logout recovery action when a saved-session check fails
• update routing documentation and focused route, landing, auth-tab, and Header tests

Why

Unauthenticated visitors were redirected straight to the auth form, so the product had no public introduction or registration-first entry point. The persisted user snapshot also cannot be treated as proof that a restored token is still valid.

User impact

Guests now get a compact CoDuels introduction with theme-matched duel imagery and direct login/registration paths. Authenticated users retain the current HomePage and profile menu after server validation. A transient non-401 session-check failure no longer leaves the Header without a way to log out.

Verification

• pnpm lint — passed (4 pre-existing warnings, no errors)
• pnpm test — passed, 30 files / 96 tests
• pnpm build with VITE_BASE_URL=__VITE_BASE_URL__ — passed
• pnpm fsd:lint — repository baseline remains 13 errors / 11 warnings; no findings point to changed files
• exact production bundle smoke-tested in installed headless Chrome:
  • non-empty application root and no uncaught/runtime errors
  • 1536 px desktop: 48 px hero heading and 984 px duel preview
  • light/dark theme-specific preview assets load and switch correctly
  • CTA has both a compatible solid background and the intended gradient
  • 600 px-tall viewport scrolls vertically (530 client / 826 scroll height)
  • 390×844 mobile layout has zero horizontal overflow
  • CTA opens registration and reload preserves it; /auth has no Header login action
  • mocked saved-token 503 exposes logout and returns to the landing
  • authenticated cold startup reaches the existing HomePage and profile menu

What to test manually

Prerequisites: a logged-out browser and one valid CoDuels account.

1. Open / at 100% browser zoom and confirm the compact scale, duel image, and three steps look balanced; reduce the window height and confirm the page scrolls.
2. Switch between light and dark themes and confirm the matching duel image appears.
3. Select Header Войти and confirm /auth opens without another Войти action in the Header.
4. Return to /, select Хочу участвовать!, confirm /auth?tab=register opens registration, then reload and confirm registration remains selected.
5. Repeat at a narrow/mobile width and confirm there is no horizontal scrolling.
6. Sign in and reload /; confirm the landing does not flash, the existing HomePage appears, Начать still opens the duel mode selection, and the profile menu remains available.

Closes #94

[chatgpt-codex-connector]

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