Add recently played to profiles

A play is recorded when a new track starts (pausing and resuming doesn't
count; returning after 10+ minutes does). Profiles show the last 10,
excluding the track playing now; 50 are kept per user. Recent plays are
free on every plan; the paid flag is renamed to fullHistory.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01MzFywujuH9TiuXbr9vjoX8

packages/shared/src/dto.ts

@@ -58,6 +58,12 @@ export interface FeaturedSongDTO {
   updatedAt: string;
 }
 
+export interface RecentPlayDTO {
+  track: TrackDTO;
+  source: NowPlayingProvider;
+  playedAt: string;
+}
+
 export interface ProfileDTO {
   user: UserSummaryDTO & { bio: string | null };
   followerCount: number;
@@ -67,6 +73,8 @@ export interface ProfileDTO {
   isSelf: boolean;
   featured: FeaturedSongDTO | null;
   nowPlaying: NowPlayingDTO | null;
+  /** Most recent first, not including the track playing right now. */
+  recent: RecentPlayDTO[];
 }
 
 export interface ConnectionDTO {