Show searching state immediately on trending landing URLs

[xenodus]

Summary

When a user lands on a search URL (for example from a trending pill), the search button and skeleton loaders now enter the searching state immediately on mount, instead of waiting for Turnstile/session bootstrap to finish first.

Problem

useSearch waited for ensureApiSession() (including Turnstile) to resolve before calling performSearch for ?s= landing URLs. During that wait the button stayed on Search, even though a search was about to start.

Solution

• Call runLandingSearchIfNeeded() at the start of the mount effect, using any cached site status for maintenance checks.
• performSearch already awaits ensureApiSession() before the API request, so Turnstile still runs in the correct place — we just show searching UI while it does.
• Remove the duplicate landing-search trigger from the ensureApiSession().then(...) path (the landingSearchHandledRef guard prevents double searches).
• If maintenance mode is known before search starts, clear the searching state and show the maintenance error instead.

Verification

Playwright check with a 3s delayed /session response on /?s=Opt:

• #searchBtn text: Searching LGS
• Button disabled: true

make test passed.

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