feat(library,home): lay libraries out as a mosaic, with favourites per category

The library overview and the home shortcut strip showed artwork of three
different shapes — square music covers, 16:9 library backdrops, 2:3 posters —
in grids that pick one box and crop everything to it. The home strip said so
in a comment: it forced `aspect="video"` on music libraries so the row would
line up, which lined it up by cutting the covers down.

Both surfaces are now justified mosaics: rows share one height and each tile is
as wide as its own artwork. `layoutMosaic` is a pure module — it packs tiles
until the height needed to fill the container drops to the target, justifies the
row by absorbing the rounding remainder into its widest tile, and deliberately
leaves the last row unstretched so one leftover tile does not inflate into a
banner. The component supplies only what the DOM knows: the measured container
width, and the artwork's *decoded* aspect ratio (via a new `onNaturalSize` on
CachedImage), committed in one debounced batch so the grid does not reshuffle
once per image as artwork lands.

Favourites gain a tile per category beside the library it belongs to, alongside
the existing cross-library entry. Which collection type maps to which category
is Jellyfin vocabulary, so it is derived in Rust — `SearchScope::for_collection_type`,
stamped onto every `Library` by a new constructor and carried over as an optional
`favoritesScope`. Deriving it in Svelte would have rebuilt the exact leak
`SearchScope::item_types` was extracted to close. A category shows one tile
however many libraries share it, and a library kind favourites do not carve up
(Live TV, channels, books) gets none.

Also corrects the requirements-count test, which the UR-074 commit left one
behind.

Spec: docs/specs/library-mosaic.md
TRACES: UR-075, UR-067 | DR-163, DR-164 | UT-158..UT-162

src/routes/+page.svelte

@@ -9,7 +9,9 @@
   import { currentMedia } from "$lib/stores/player";
   import HeroBanner from "$lib/components/home/HeroBanner.svelte";
   import Carousel from "$lib/components/home/Carousel.svelte";
-  import MediaCard from "$lib/components/library/MediaCard.svelte";
+  import MosaicGrid from "$lib/components/library/MosaicGrid.svelte";
+  import MosaicTile from "$lib/components/library/MosaicTile.svelte";
+  import { assumedLibraryRatio } from "$lib/components/library/libraryMosaic";
   import { useScrollRestore } from "$lib/utils/scrollContainer";
   import type { MediaItem, Library } from "$lib/api/types";
 
@@ -113,6 +115,15 @@
     $libraries.filter((lib) => lib.collectionType !== "playlists")
   );
 
+  // The shortcut strip is a mosaic row: one height, each tile as wide as its own
+  // artwork. It used to force 16:9 on everything so square music covers lined up
+  // with wide backdrops — which lined them up by cropping the covers.
+  // TRACES: UR-075 | DR-163
+  const LIBRARY_STRIP_HEIGHT = 132;
+  const libraryTiles = $derived(
+    shortcutLibraries.map((lib) => ({ key: lib.id, ratio: assumedLibraryRatio(lib), library: lib }))
+  );
+
   function handleLibraryClick(lib: Library) {
     // Mirror /library routing: dedicated landing pages need currentLibrary set.
     library.setCurrentLibrary(lib);
@@ -166,19 +177,25 @@
     {#if shortcutLibraries.length > 0}
       <div>
         <h2 class="text-xl font-bold text-white mb-4 px-4">Your Libraries</h2>
-        <div class="flex gap-4 overflow-x-auto px-4 pb-2 items-start">
-          {#each shortcutLibraries as lib (lib.id)}
-            <div class="flex-shrink-0">
-              <!-- Uniform 16:9 artwork so music (square) and video libraries
-                   line up at the same height in this mixed row. -->
-              <MediaCard
-                item={lib}
-                size="medium"
-                aspect="video"
-                onclick={() => handleLibraryClick(lib)}
+        <div class="px-4">
+          <MosaicGrid
+            items={libraryTiles}
+            layout="strip"
+            targetHeight={LIBRARY_STRIP_HEIGHT}
+            gap={12}
+          >
+            {#snippet tile(entry)}
+              <MosaicTile
+                label={entry.library.name}
+                width={entry.width}
+                height={entry.height}
+                itemId={entry.library.id}
+                imageTag={entry.library.imageTag}
+                onRatio={entry.reportRatio}
+                onclick={() => handleLibraryClick(entry.library)}
               />
-            </div>
-          {/each}
+            {/snippet}
+          </MosaicGrid>
         </div>
       </div>
     {/if}