refactor(frontend): each page fills the floating header itself; the header knows no page

The header used to pick its pills by `page === …` and import five module controls, and Plex's
Discover/Browse toggle needed a context bridge to reach the sub-view that lives in PlexBrowse.
Now the header is an empty band: PageShell hands its root box out as a slot, a page portals its
own pills into it (PageHeader), and the palette's Jump-to pill shows where no page does
(PageHeaderDefault, rendered inside the page's Suspense so a loading page shows no stand-in).
Plex's toggles take the sub-view as a prop; PlexViewBridge and its context are gone, and with
them the header's five layer suppressions.

No visible change: every header pill's box measured identical against the previous build on eight
pages, in Hungarian and English.

docs/DESIGN.md

@@ -275,7 +275,9 @@ Also in force:
 - **Page chrome (B4):** a page's tabs and filters sit in ONE sticky band of the page colour, with the fade
   under it (below). Below ~600px of height the filter row folds into one "Filters · n" button. Every page has
   a visually hidden `h1`; the nav rail and the browser tab title are the visible identity. [WCAG 2.4.6]
-  Built as: the band is `PageShell`'s toolbar slot (`PageToolbar`), above the one scroller. The band
+  Built as: the band is `PageShell`'s toolbar slot (`PageToolbar`), above the one scroller; the floating
+  header over it is its header slot (`PageHeader`: the page's own pills, the palette's Jump-to pill where a
+  page has none, `PageHeaderDefault`). The band
   holds controls only: an intro paragraph scrolls with the content (in the band it ate three lines of a
   short window). The fold is `useFilterFold` + `FilterFoldButton`: the same row
   shown or hidden in place, never copied into a popover. The hidden `h1` is `PageShell`'s `title`; a