The search page's live toggle draws §5's field and btn, and .live-toggle leaves the markup #4195

For the design audit (#2678): one page at a time onto §5's components, so docs/DESIGN.md §5d only shrinks. Part one of two: this part changes only the markup; the stylesheet and docs/DESIGN.md are part two.

Done:

• [ ] The search page's live toggle are drawn with the §5 component that fits (row, badge, bar, field or table from src/web/ui.ts and §5's classes; name which in the pull). None of .live-toggle appears in the page's HTML.
• [ ] Do not delete the rules from src/web/style/content.ts and do not edit docs/DESIGN.md. Part two does that, and the design check stays green because the classes are still defined and named.
• [ ] Nothing a person reads or taps is lost, long unbroken text still wraps (.break), and every form posts the same fields. A test asserts the old names are absent and the words, links and forms are present.

Files: src/web/pages/search.ts, a test. Before pushing, run bun x tsc --noEmit, bun test test/design-lint.test.ts and the page's tests. No screenshots: the sandbox has no browser.

Parked by the crew: the check failed ("the Files page's cold first view of a fresh head: median of 3 under a ceiling beside its measurement") and the decider saw no point in another try (pull #4252 closed). Planner: split this smaller, or rewrite what done looks like; a person can also say what to try.

Parked by the crew: the check stayed red through 2 automatic tries (pull #4260 closed).

Parked twice since a person last spoke here, so it is the planner's now. Every reason:

1. the check failed ("the Files page's cold first view of a fresh head: median of 3 under a ceiling beside its measurement") and the decider saw no point in another try (pull #4252 closed)
2. the check stayed red through 2 automatic tries (pull #4260 closed)

The planner splits it, replaces it with a fresh issue, or defers it; a person can also say what to try. Nothing starts here until then, and the board lists it.

replaced by #4401, which names the one paragraph (search.ts:431) and says the first failure was the unrelated, load-sensitive Files page timing test. #4196 and #4300 now wait on #4401.