Optimize home/library loading and SQLite query performance

- Replace home preview N+1 queries with a single window-function batch query
- Cache library previews and series card lists (15s TTL, shared with media cache)
- Tune SQLite: larger page cache, mmap, wal_autocheckpoint, ANALYZE on migrate
- Defer history fetch on library page until last_played sort is selected
- Yield to browser between paginated library loads to keep UI responsive

Co-authored-by: truewhile <truewhile@users.noreply.github.com>

internal/database/schema_migration.go

@@ -24,11 +24,19 @@ func AutoMigrate(db *gorm.DB) error {
 		return err
 	}
 	if isSQLite(db) {
-		return ensureMediaSearchIndex(db)
+		if err := ensureMediaSearchIndex(db); err != nil {
+			return err
+		}
+		return ensureSQLiteQueryOptimizer(db)
 	}
 	return nil
 }
 
+func ensureSQLiteQueryOptimizer(db *gorm.DB) error {
+	// Refresh planner statistics so indexes on large media tables are used.
+	return db.Exec("ANALYZE").Error
+}
+
 func ensurePostgresColumnCompatibility(db *gorm.DB) error {
 	if !isPostgres(db) {
 		return nil