fix(reactions): backgammon players can send reactions in online games

isMatchParticipant() knew only ludo and domino matches, so every reaction
poll in an online backgammon game answered 403 and nothing reached the
opponent. Backgammon seats come from players or the colour columns.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

api/match-chat.php

@@ -216,11 +216,15 @@ function isMatchParticipant($sdb, string $gameKey, string $matchId, string $user
     $table = [
         'ludo'       => 'ludo_matches',
         'domino'     => 'domino_matches',
+        'backgammon' => 'backgammon_matches',
     ][$gameKey] ?? null;
     if (!$table) return false;
 
-    $rows = $sdb->get($table, ['id' => 'eq.' . $matchId, 'select' => 'players', 'limit' => 1]);
+    // Backgammon rows may seat players by colour instead of (or as well as) the list.
+    $select = $gameKey === 'backgammon' ? 'players,white_player_id,black_player_id' : 'players';
+    $rows = $sdb->get($table, ['id' => 'eq.' . $matchId, 'select' => $select, 'limit' => 1]);
     if (!is_array($rows) || empty($rows) || isset($rows['error'])) return false;
+    if (($rows[0]['white_player_id'] ?? null) === $userId || ($rows[0]['black_player_id'] ?? null) === $userId) return true;
 
     $players = $rows[0]['players'] ?? [];
     if (is_string($players)) $players = json_decode($players, true) ?: [];