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/api/bindings.ts

@@ -1858,7 +1858,24 @@ imageId?: string | null; backdropImageTags?: string[] | null; parentBackdropImag
  * typo or an unhandled kind is a compile error on the frontend, not a silent
  * runtime miss across ~127 comparison sites.
  */
-export type MediaKind = "track" | "album" | "artist" | "playlist" | "movie" | "series" | "season" | "episode" | "person" | "channel" | "folder" | 
+export type MediaKind = "track" | "album" | "artist" | "playlist" | "movie" | "series" | "season" | "episode" | "person" | 
+/**
+ * A channel *container* the user drills into (Jellyfin `Channel`).
+ */
+"channel" | "folder" | 
+/**
+ * A live TV channel — playable, but a live stream with no seekable
+ * timeline (no resume/seek). Jellyfin `TvChannel`/`LiveTvChannel`.
+ */
+"liveChannel" | 
+/**
+ * A playable leaf inside a channel (Jellyfin `ChannelFolderItem` that is
+ * not itself a folder) — e.g. a plugin-channel VOD item that has no
+ * dedicated item type but carries its own media streams. Playable and
+ * seekable, unlike `LiveChannel`. Distinct from `Channel` (the container)
+ * and from `Other` so the UI can route it to playback.
+ */
+"channelItem" | 
 /**
  * A kind we do not model explicitly. Reached only for provider item types
  * that map to nothing meaningful; consumers treat it like an opaque

src/lib/api/types.ts

@@ -14,6 +14,7 @@ export type {
   Library,
   LiveStreamInfo,
   MediaItem,
+  MediaKind,
   MediaSource,
   MediaStream,
   Person,