Add section filter chips to search results

[Anarchydr]

Added category filter chips to the local search modal so users can narrow down results to a specific wiki section (like Gaming, Audio, or Reading).

Once you type a query, filter chips showing live match counts pop up under the search bar. Picking a section filters the results, "All" resets it, and your selection is remembered in localStorage.

A few notes:

• Categories are generated directly from the sidebar, so any sidebar renames update automatically. If Wiki and Tools share a page (like /audio#audio-tools), they get grouped under Wiki.
• Filtering happens on the in-memory results before pagination. Switching categories doesn't re-trigger the search index query, which keeps highlights, counts, keyboard navigation, and "Show more" working smoothly.
• If a section turns up zero matches, it shows No results in <section> — Show all sections so it's clear the search itself didn't fail.
• Ran pnpm docs:build, pnpm lint, and prettier check
• Tested filtering manually across exact, fuzzy, and URL search modes

[flowerey]

LGTM if it works. It is good that you didn't hardcode the chips :)