feat(api): extend ArtistRef/AlbumRef + add HomePayload for M6a

- ArtistRef gains SortName and CoverURL fields
- AlbumRef gains SortTitle field
- albumRefFrom now populates SortTitle from dbq.Album.SortTitle
- artistRefFrom now populates SortName from dbq.Artist.SortName
- New artistRefFromCovered helper builds CoverURL from nullable cover_album_id
- New HomePayload view type for GET /api/home response body

internal/api/convert.go

@@ -75,16 +75,31 @@ func streamURL(trackID pgtype.UUID) string {
 	return "/api/tracks/" + uuidToString(trackID) + "/stream"
 }
 
-// artistRefFrom projects a dbq.Artist into an ArtistRef. albumCount must be
+// artistRefFrom projects a dbq.Artist into an ArtistRef without cover.
-// pre-computed by the caller (one query per artist in lists).
+// albumCount must be pre-computed by the caller. Used by code paths that
+// don't have a representative-album lookup at hand (artist detail, search,
+// liked-artists list).
 func artistRefFrom(a dbq.Artist, albumCount int) ArtistRef {
 	return ArtistRef{
 		ID:         uuidToString(a.ID),
 		Name:       a.Name,
+		SortName:   a.SortName,
 		AlbumCount: albumCount,
 	}
 }
 
+// artistRefFromCovered projects a dbq.Artist into an ArtistRef with the
+// derived CoverURL populated from a representative album id (nullable).
+// Used by /api/home and /api/artists?sort=alpha which carry the lookup
+// in the same query.
+func artistRefFromCovered(a dbq.Artist, albumCount int, coverAlbumID pgtype.UUID) ArtistRef {
+	ref := artistRefFrom(a, albumCount)
+	if coverAlbumID.Valid {
+		ref.CoverURL = coverURL(coverAlbumID)
+	}
+	return ref
+}
+
 // albumRefFrom projects a dbq.Album into an AlbumRef. artistName must be
 // pre-resolved because Album only carries artist_id. trackCount and
 // durationSec may be 0 when the caller does not compute them.
@@ -92,6 +107,7 @@ func albumRefFrom(a dbq.Album, artistName string, trackCount, durationSec int) A
 	return AlbumRef{
 		ID:          uuidToString(a.ID),
 		Title:       a.Title,
+		SortTitle:   a.SortTitle,
 		ArtistID:    uuidToString(a.ArtistID),
 		ArtistName:  artistName,
 		Year:        yearFromDate(a.ReleaseDate),

internal/api/types.go

@@ -36,18 +36,26 @@ type Page[T any] struct {
 }
 
 // ArtistRef is the lightweight artist shape used in lists and search results.
+// SortName is exposed so the SPA's alphabetical-grid divider can group rows
+// by the catalogue sort order ("The Beatles" → "B"). CoverURL is derived from
+// a representative album (most-recent with cover_art_path); empty when the
+// artist's discography has no cover art.
 type ArtistRef struct {
 	ID         string `json:"id"`
 	Name       string `json:"name"`
+	SortName   string `json:"sort_name"`
 	AlbumCount int    `json:"album_count"`
+	CoverURL   string `json:"cover_url"`
 }
 
 // AlbumRef is the lightweight album shape used in lists, artist details,
-// and search results. CoverURL points to /api/albums/{id}/cover which
+// and search results. SortTitle is exposed so the SPA's alphabetical-grid
-// Plan 3 implements.
+// divider can group rows by sort order ("The Wall" → "W"). CoverURL points
+// to /api/albums/{id}/cover.
 type AlbumRef struct {
 	ID          string `json:"id"`
 	Title       string `json:"title"`
+	SortTitle   string `json:"sort_title"`
 	ArtistID    string `json:"artist_id"`
 	ArtistName  string `json:"artist_name"`
 	Year        int    `json:"year,omitempty"`
@@ -92,3 +100,15 @@ type SearchResponse struct {
 	Albums  Page[AlbumRef]  `json:"albums"`
 	Tracks  Page[TrackRef]  `json:"tracks"`
 }
+
+// HomePayload is the response body of GET /api/home. Field counts:
+// 50 (recently_added) / 25 (rediscover_albums) / 25 (rediscover_artists)
+// / 75 (most_played) / 25 (last_played). All slices are non-nil at JSON
+// encode time so empty sections render as [] rather than null.
+type HomePayload struct {
+	RecentlyAddedAlbums []AlbumRef  `json:"recently_added_albums"`
+	RediscoverAlbums    []AlbumRef  `json:"rediscover_albums"`
+	RediscoverArtists   []ArtistRef `json:"rediscover_artists"`
+	MostPlayedTracks    []TrackRef  `json:"most_played_tracks"`
+	LastPlayedArtists   []ArtistRef `json:"last_played_artists"`
+}