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-tauri/src/repository/offline.rs

@@ -864,7 +864,7 @@ impl MediaRepository for OfflineRepository {
 
         let genres = genre_set
             .into_iter()
-            .map(|name| Genre { id: name.clone(), name })
+            .map(|name| Genre { id: name.clone(), name, album_count: None })
             .collect();
 
         Ok(genres)

src-tauri/src/repository/online.rs

@@ -811,7 +811,12 @@ impl MediaRepository for OnlineRepository {
     }
 
     async fn get_genres(&self, parent_id: Option<&str>) -> Result<Vec<Genre>, RepoError> {
-        let mut endpoint = format!("/Genres?UserId={}", self.user_id);
+        // Ask Jellyfin to scope counts to albums and include them, so the
+        // frontend can rank genres by popularity without probing each one.
+        let mut endpoint = format!(
+            "/Genres?UserId={}&IncludeItemTypes=MusicAlbum&Recursive=true&Fields=ItemCounts",
+            self.user_id
+        );
 
         if let Some(pid) = parent_id {
             endpoint.push_str(&format!("&ParentId={}", pid));
@@ -828,17 +833,34 @@ impl MediaRepository for OnlineRepository {
         struct JellyfinGenre {
             id: String,
             name: String,
+            // Which count field Jellyfin populates for a genre under
+            // Fields=ItemCounts varies by server/version: scoped queries may
+            // fill AlbumCount, others only ChildCount. Read whichever is
+            // present so ranking still works. Absent on servers that ignore
+            // Fields=ItemCounts entirely, so all stay optional.
+            album_count: Option<u32>,
+            child_count: Option<u32>,
         }
 
         let response: GenresResponse = self.get_json(&endpoint).await?;
-        Ok(response
+        let genres: Vec<Genre> = response
             .items
             .into_iter()
             .map(|g| Genre {
                 id: g.id,
                 name: g.name,
+                album_count: g.album_count.or(g.child_count),
             })
-            .collect())
+            .collect();
+
+        let with_counts = genres.iter().filter(|g| g.album_count.is_some()).count();
+        log::debug!(
+            "get_genres: {} genres, {} carry counts (AlbumCount/ChildCount)",
+            genres.len(),
+            with_counts
+        );
+
+        Ok(genres)
     }
 
     async fn search(

src-tauri/src/repository/types.rs

@@ -255,6 +255,10 @@ pub struct PlaybackInfo {
 pub struct Genre {
     pub id: String,
     pub name: String,
+    /// Number of albums tagged with this genre, when the backend can supply it
+    /// (online only). Lets the frontend rank/pick genres without probing each
+    /// one. `None` when unknown (e.g. offline).
+    pub album_count: Option<u32>,
 }
 
 /// Image type