feat(library): genre sliders, artist links, and navigation utils

- music landing: diverse per-genre album sliders (online counts /
  offline wide-probe fallback) and home-screen library shortcuts
- add ArtistLinks component and shared navigation/genreDiversity utils
- player/playback-mode refinements across Rust and frontend

src/routes/+page.svelte

@@ -4,11 +4,13 @@
   import { platform } from "@tauri-apps/plugin-os";
   import { auth, isAuthenticated } from "$lib/stores/auth";
   import { home } from "$lib/stores/home";
+  import { library, libraries } from "$lib/stores/library";
   import { isServerReachable } from "$lib/stores/connectivity";
   import { currentMedia } from "$lib/stores/player";
   import HeroBanner from "$lib/components/home/HeroBanner.svelte";
   import Carousel from "$lib/components/home/Carousel.svelte";
-  import type { MediaItem } from "$lib/api/types";
+  import MediaCard from "$lib/components/library/MediaCard.svelte";
+  import type { MediaItem, Library } from "$lib/api/types";
 
   // Track if we've done an initial load (plain variable, not reactive)
   let hasLoadedOnce = false;
@@ -34,6 +36,9 @@
 
     if ($isAuthenticated) {
       await home.loadHomeSections();
+      if ($libraries.length === 0) {
+        await library.loadLibraries();
+      }
       hasLoadedOnce = true;
     }
   });
@@ -68,6 +73,31 @@
     }
   }
 
+  // Playlist libraries live inside the Music landing page, not as top-level shortcuts.
+  const shortcutLibraries = $derived(
+    $libraries.filter((lib) => lib.collectionType !== "playlists")
+  );
+
+  function handleLibraryClick(lib: Library) {
+    // Mirror /library routing: dedicated landing pages need currentLibrary set.
+    library.setCurrentLibrary(lib);
+    switch (lib.collectionType) {
+      case "music":
+        goto("/library/music");
+        break;
+      case "tvshows":
+        goto("/library/tv");
+        break;
+      case "movies":
+        goto("/library/movies");
+        break;
+      default:
+        library.clearGenres();
+        goto("/library");
+        break;
+    }
+  }
+
   const heroItems = $derived($home.heroItems);
   const resumeItems = $derived($home.resumeItems.filter(
     i => i.type === "Movie" || i.type === "Episode"
@@ -92,6 +122,24 @@
       <HeroBanner items={heroItems} />
     {/if}
 
+    <!-- Your Libraries: quick jump into each dedicated landing page -->
+    {#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">
+          {#each shortcutLibraries as lib (lib.id)}
+            <div class="flex-shrink-0">
+              <MediaCard
+                item={lib}
+                size="medium"
+                onclick={() => handleLibraryClick(lib)}
+              />
+            </div>
+          {/each}
+        </div>
+      </div>
+    {/if}
+
     <!-- Next Movie -->
     {#if resumeMovies.length > 0}
       <Carousel