feat(nav): the live YouTube search and Home's budget are named in the address

A YouTube search is `?yt=<term>` (+ `ytn` for a non-default count), so a reload, a link
or Back/Forward reopens it. It runs by itself only where it costs no quota: the free page
scrape, a search asked for in this document, or results still cached. An API search
reopened any other way shows its term and waits for "Search YouTube again".

Home's time budget is `hb`; the question's draw stays on the history entry.

An e2e spec opens every page's bookmark in a fresh browser context; CLAUDE.md and
docs/development.md name the module URL codec as the place for view state.

docs/development.md

@@ -48,6 +48,12 @@ A frontend page is one folder, `frontend/src/modules/<id>/` (the layering is in
    only its store (a `…Provider` / `…Store` file); the page and the rail load lazily. `urlKeys` names every
    address-bar key its view writes (the URL is the view: a bookmark reopens it), its list kept in `lib/` beside
    its codec; the shell clears them on a page switch and opens a page without another page's keys.
+   Every setting the page shows — a tab, a sort, a filter, a search, the item open in it — goes there: a codec
+   in `lib/<id>UrlState.ts` (read the params into the view, write the view as updates, a default left out),
+   written with `useUrlMirror` (a sub-view through `useHistorySubview`'s `url`, an overlay through
+   `useBackToClose`'s), read back first on mount (a link wins over anything remembered). Add its round trip to
+   `e2e/bookmark.spec.ts`. Only what an address cannot promise to reopen stays out, said in its codec (Home's
+   draw, `lib/homeUrlState`).
 3. `index.ts`, the module's public face: the definition, and only what other folders must read (its store's
    hooks). Another folder reaches the module through this file or not at all.
 4. The id in `lib/urlState`'s `PAGES`, and the definition in `features/navigation/moduleRegistry.ts`, in