domain: flip catalog frontend off Jellyfin item-type strings (phase 2a)

Migrate catalog MediaItem consumers from stringly item.type ("Audio",
"MusicAlbum", …) to the neutral item.kind enum across all classification
logic: home, library detail, player routing, artist/person/related/genre
components, tv store.

Model refinements found during migration (each a real distinction the
flat item_type collapsed):
- MediaKind::LiveChannel — live TV (playable, non-seekable) vs
- MediaKind::ChannelItem — channel VOD leaf (playable, seekable) vs
- MediaKind::Channel — channel container (drill-in).
  TvChannel->LiveChannel, non-folder ChannelFolderItem->ChannelItem.

RelatedItemsSection and GenreTags props migrated from Jellyfin type
strings to MediaKind; MediaKind re-exported from api/types.

Deferred by design: display {item.type} text, ResultsCounter labels,
Person.type (role), stream.type (phase 4), and all runTimeTicks/tick math
(coupled to playbackPositionTicks — phase 3). Old fields still dual-carried
so nothing breaks.

Rust 456 + 7 domain tests, frontend 644 tests, check clean.

src/lib/components/library/RelatedItemsSection.svelte

@@ -2,12 +2,12 @@
   import { onMount } from "svelte";
   import { goto } from "$app/navigation";
   import { auth } from "$lib/stores/auth";
-  import type { MediaItem, Person } from "$lib/api/types";
+  import type { MediaItem, MediaKind, Person } from "$lib/api/types";
   import MediaCard from "./MediaCard.svelte";
 
   interface Props {
     currentItemId: string;
-    itemType: "Movie" | "Series" | "MusicAlbum" | "Audio";
+    itemKind: MediaKind;
     genres?: string[];
     people?: Person[];
     artistIds?: string[];
@@ -16,7 +16,7 @@
 
   let {
     currentItemId,
-    itemType,
+    itemKind,
     genres = [],
     people = [],
     artistIds = [],
@@ -45,9 +45,9 @@
 
       let items: MediaItem[] = [];
 
-      // First, try to use the Jellyfin Similar Items API (preferred method)
+      // First, try to use the Similar Items API (preferred method)
       // This works for Movies and Series (most common cases)
-      if (["Movie", "Series"].includes(itemType)) {
+      if (itemKind === "movie" || itemKind === "series") {
         try {
           const result = await repo.getSimilarItems(currentItemId, limit);
           items = result.items.filter(item => item.id !== currentItemId);
@@ -65,10 +65,14 @@
       // Fallback: Load by genres using search (works for all item types)
       if (genres && genres.length > 0) {
         try {
-          // Search by first genre to find related items
+          // Search by first genre to find related items. This single-kind query
+          // maps the neutral kind to the concrete Jellyfin item type it needs.
           const searchTerm = genres[0];
+          const itemTypeForKind: Record<string, string> = {
+            movie: "Movie", series: "Series", album: "MusicAlbum", track: "Audio", artist: "MusicArtist",
+          };
           const result = await repo.search(searchTerm, {
-            includeItemTypes: itemType === "MusicAlbum" ? ["MusicAlbum"] : itemType === "Audio" ? ["Audio"] : [itemType],
+            includeItemTypes: [itemTypeForKind[itemKind] ?? "Movie"],
             limit: limit * 2
           });
 
@@ -79,7 +83,7 @@
       }
 
       // For music albums, also try to load by artist (if we don't have enough from similar API)
-      if (itemType === "MusicAlbum" && artistIds && artistIds.length > 0 && items.length === 0) {
+      if (itemKind === "album" && artistIds && artistIds.length > 0 && items.length === 0) {
         try {
           // Search for other albums by artist name from first artist
           const result = await repo.search(artistIds[0], {
@@ -109,14 +113,14 @@
   }
 
   function getTitle(): string {
-    switch (itemType) {
-      case "Movie":
+    switch (itemKind) {
+      case "movie":
         return "Related Movies";
-      case "Series":
+      case "series":
         return "Related Shows";
-      case "MusicAlbum":
+      case "album":
         return "Related Albums";
-      case "Audio":
+      case "track":
         return "Related Tracks";
       default:
         return "Related Items";
@@ -133,7 +137,7 @@
 
   {#if loading}
     <!-- Skeleton loading state -->
-    {@const isMusicContent = itemType === "MusicAlbum" || itemType === "Audio"}
+    {@const isMusicContent = itemKind === "album" || itemKind === "track"}
     <div class="grid grid-cols-2 md:grid-cols-6 gap-4">
       {#each Array(6) as _}
         <div class="animate-pulse">