fix(websearch): consolidate to single tile + fix multi-word command query bleed
Two related changes to the websearch feature:
1. Delete orphan `background.html` / `background.js`. The manifest already
collapsed to a single resident `home` tile in earlier work; `home.js`
already owns engine state + UI. The background files were unreferenced
from the manifest but lingering on disk. All 10 websearch desktop
tests green after deletion.
2. Fix `cmd → web search` (no query) opening the default engine for the
literal string "search". Root cause in `extractSearchQuery`: when
`ctx.typed === ctx.name === "web search"`, steps 1-4 returned no query,
then the step-5 fallback (`typed.indexOf(' ')`) treated the second word
of the command name as the query. Fix: only run the step-5 fallback
when `ctx.name` is missing - preserves its "name unknown" intent
without bleeding multi-word command names. New Playwright regression
test in `tests/desktop-serial/websearch-cmd.spec.ts` types
"web search" with no query and asserts the home tile is shown
instead of a search-results URL.
Also `docs/tasks.md` updates: replaced the websearch consolidation task
with audit findings (tags + lists are next candidates), added a
2026-04-27 pruned-log entry, and recorded two new bugs - undo close
window (cmd+shift+t) is unreliable, and page-load failures (e.g.
metikmusic.com) show a blank white page forever instead of a
Peek-branded error UI.