Wire local search for docs.fallout.build

[ChrisonSimtian]

Context

The docs site at https://docs.fallout.build/ has no search. The original done-when checklist on #41 called for "Search works (Algolia/etc.)".

Decision (2026-05-26): going with local search via `@easyops-cn/docusaurus-search-local` — self-contained, no third-party dependency, search index built at site-build time and shipped with the static assets. At the current docs volume the search-quality gap vs. Algolia doesn't matter; we can switch to Algolia later if traffic and content scale warrants the upgrade.

Done when

• `@easyops-cn/docusaurus-search-local` added to Falloutdocs and wired in `docusaurus.config.ts`.
• Search box appears in the docs site navbar and returns relevant results.
• Build still completes in reasonable time and the bundle size is acceptable (rough target: site total < 5 MB, search index a few hundred KB).

Notes

• All wiring lives in Falloutdocs, not this repo.
• If we ever want to flip to Algolia later, the application URL is https://docsearch.algolia.com/apply.

Refs

• [P7] Documentation site migration #41 — parent docs-site migration issue (closed; this is one of three follow-ups).

[ChrisonSimtian]

Closing summary (the PR auto-closed this before I could add the note):

What landed: Falloutdocs #4 wires `@easyops-cn/docusaurus-search-local@0.54.1` as a Docusaurus theme. Index is generated at build time and ships with the static assets — no external service or AI dependency. (0.54.1 pin is deliberate: the 0.55.x line added `open-ask-ai` as a hard peer dependency for an AI Q&A widget we don't want.)

Confirmed live:

• Search input rendered in the navbar (in SSR'd HTML, not client-only).
• `https://docs.fallout.build/search-index.json\` returns 200.
• `https://docs.fallout.build/search\` (dedicated results page) resolves.
• Falloutdocs deploy: run 26442792705 — green.

Out-of-scope follow-up noticed during this work: filed as #196 — `docs/introduction.md` has an MDX comment leaking into the page `` and uses stale NUKE-branded commands in the Fast Track section.