fix(docs/search): handle search index loading and failure states

[Anuragp22]

Summary

• Replaces the misleading "No results found" empty state shown when users searched before the MiniSearch index finished loading. The search now shows "Loading search index..." and replays the query automatically once the index is ready.
• Renders a distinct "Failed to load search index. Please refresh." message on fetch error so the loading state does not persist indefinitely.

Fixes #3180.

Open question for review

The failure-state message is not in the issue description but is a necessary consequence of the loading-state change. Without it, a failed fetchSearchIndex would leave "Loading..." showing forever. Open to dropping or rephrasing if a different approach is preferred.

The pre-existing openSearchUI() call to updateSearchResults([]) (which renders "No results found" on open before any typing) is out of scope and untouched.

Test plan

src/docs/src/assets/js/search.js has no existing unit tests, so this change is verified manually. Built and served locally (npm run build && npm run serve in src/docs):

• Normal speed: search results render as before, no flash of loading state.
• 3G throttle, type before /index.json loads: "Loading search index..." appears, results auto-render when the index lands without retyping.
• /index.json returning 404: brief "Loading..." then "Failed to load search index. Please refresh."
• 3G throttle, type then backspace to empty input before the index loads: pending query is cleared, no stale results fire when the index arrives.

[CLAassistant]

All committers have signed the CLA.