feat(slice-2): Landing + Sign-in screens, entry routing, API client (§5.1/5.2/6.5)

Two-step email + one-time-code sign-in behind both doors; pure entry-routing rule unit-
tested with Vitest (§6.8); storefront routing reaches a SLICE-2 signed-in placeholder with
sign-out (PUC-9). check.sh now runs the frontend unit tests.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

scripts/check.sh

@@ -34,4 +34,7 @@ echo "==> backend tests (pytest)"
 echo "==> frontend typecheck + build"
 ( cd "$repo_root/frontend" && npm run build )
 
+echo "==> frontend unit tests (vitest)"
+( cd "$repo_root/frontend" && npm test )
+
 echo "==> all gates green"