feat: AI-game refinements (GCG, your_turn, admin, metrics)

Follow-ups on the honest-AI game, same PR:
- GCG export labels the robot seat "AI" instead of its pool name (ExportGCG
  overrides via accounts.IsRobot); the in-app 🤖 is unchanged.
- vs_ai games emit no your_turn (the robot replies instantly, so it would be
  redundant); opponent_moved still advances the UI.
- Admin console shows the AI flag: a 🤖 column in /games and an "AI game" line
  on the game card (GameRow/GameDetailView gain VsAI).
- games_started_total / games_abandoned_total gain a vs_ai attribute; the
  Grafana Game-domain dashboard splits started/abandoned into human and AI
  panels.

Tests: metrics unit (vs_ai split); integration (no your_turn, GCG "AI").

backend/internal/game/metrics.go

@@ -101,15 +101,22 @@ func phaseOf(moveCount int) string {
 	}
 }
 
-// recordStarted counts one started game of variant.
-func (m *gameMetrics) recordStarted(ctx context.Context, v engine.Variant) {
-	m.started.Add(ctx, 1, variantAttr(v))
+// recordStarted counts one started game of variant, split by whether it is an
+// honest-AI game (the vs_ai attribute), so AI and human games chart separately.
+func (m *gameMetrics) recordStarted(ctx context.Context, v engine.Variant, vsAI bool) {
+	m.started.Add(ctx, 1, gameKindAttr(v, vsAI))
 }
 
 // recordAbandoned counts one seat dropped by the turn-timeout sweeper in a game of
-// variant.
-func (m *gameMetrics) recordAbandoned(ctx context.Context, v engine.Variant) {
-	m.abandoned.Add(ctx, 1, variantAttr(v))
+// variant, split by the vs_ai attribute (an AI game's abandon is the 7-day rule).
+func (m *gameMetrics) recordAbandoned(ctx context.Context, v engine.Variant, vsAI bool) {
+	m.abandoned.Add(ctx, 1, gameKindAttr(v, vsAI))
+}
+
+// gameKindAttr is the (variant, vs_ai) attribute set shared by the started and
+// abandoned counters so AI and human games are split on the same labels.
+func gameKindAttr(v engine.Variant, vsAI bool) metric.MeasurementOption {
+	return metric.WithAttributes(attribute.String("variant", v.String()), attribute.Bool("vs_ai", vsAI))
 }
 
 // variantAttr is the shared "variant" attribute option, usable for both Record and