feat(player): a video's related videos, on demand beside it

The player shows what YouTube lists beside the video, without what the
user has watched or hidden. Wide, a Related tab beside the description;
stacked, a button beside the info opens them in a drawer. A row plays in
the same player (Back returns) and the list stays the opened video's.
A switch picks on-topic or Hungarian-trending lists, kept on the account.

Each related row says whether the user follows its channel; the row is
the video card's narrow form with its whole menu. VideoMenu moves to
features/video, where the player can reach it.

frontend/src/lib/api/feed.ts

@@ -35,6 +35,21 @@ export function isResettable(v: Pick<Video, "status" | "position_seconds">): boo
   return v.status !== "new" || v.position_seconds > 0;
 }
 
+/** A video's related videos, in the locale YouTube fills the list in: on the video's topic, or with
+ *  what trends in Hungary (the server's `RELATED_REGIONS`). */
+export type RelatedRegion = "topical" | "hu";
+
+/** A row of a related list: a feed row that also says whether the user follows its channel. */
+export interface RelatedVideo extends Video {
+  followed: boolean;
+}
+
+export interface RelatedResponse {
+  items: RelatedVideo[];
+  has_more: boolean;
+  next_cursor: string | null;
+}
+
 export interface VideoDetail {
   id: string;
   description: string | null;
@@ -235,6 +250,21 @@ export const feedApi = {
     if (limit) p.set("limit", String(limit));
     return req(`/api/search/youtube?${p.toString()}`, {}, { quiet: true });
   },
+  // The videos YouTube shows beside this one, without what the user has watched or hidden. `quiet`
+  // for the same reason as the search: the list renders its refusal (the day's cap, YouTube) inline.
+  related: (
+    videoId: string,
+    region: RelatedRegion,
+    cursor: string | null,
+  ): Promise<RelatedResponse> => {
+    const p = new URLSearchParams({ region });
+    if (cursor) p.set("cursor", cursor);
+    return req(
+      `/api/search/related/${encodeURIComponent(videoId)}?${p.toString()}`,
+      {},
+      { quiet: true },
+    );
+  },
   // Discard a set of live-search results "as if never added" (drops your search-finds + deletes
   // the now-orphaned, un-kept videos). Returns how many videos were removed.
   clearSearch: (videoIds: string[]): Promise<{ removed: number }> =>