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_test.go

@@ -20,10 +20,12 @@ func TestGameMetrics(t *testing.T) {
 	meter := sdkmetric.NewMeterProvider(sdkmetric.WithReader(reader)).Meter("test")
 	m := newGameMetrics(meter)
 
-	m.recordStarted(ctx, engine.VariantEnglish)
-	m.recordStarted(ctx, engine.VariantEnglish)
-	m.recordStarted(ctx, engine.VariantRussianScrabble)
-	m.recordAbandoned(ctx, engine.VariantErudit)
+	m.recordStarted(ctx, engine.VariantEnglish, false)
+	m.recordStarted(ctx, engine.VariantEnglish, false)
+	m.recordStarted(ctx, engine.VariantRussianScrabble, false)
+	m.recordStarted(ctx, engine.VariantEnglish, true) // an honest-AI game
+	m.recordAbandoned(ctx, engine.VariantErudit, false)
+	m.recordAbandoned(ctx, engine.VariantEnglish, true) // an AI game abandoned (the 7-day rule)
 	m.recordReplay(ctx, engine.VariantEnglish, time.Now().Add(-time.Millisecond))
 	m.recordValidate(ctx, engine.VariantRussianScrabble, time.Now().Add(-time.Millisecond))
 	m.recordMoveDuration(ctx, engine.VariantEnglish, 3, 5*time.Second)
@@ -35,11 +37,15 @@ func TestGameMetrics(t *testing.T) {
 	}
 
 	started := counterByAttr(t, rm, "games_started_total", "variant")
-	if started["scrabble_en"] != 2 || started["scrabble_ru"] != 1 {
-		t.Errorf("games_started_total = %v, want scrabble_en:2 scrabble_ru:1", started)
+	if started["scrabble_en"] != 3 || started["scrabble_ru"] != 1 {
+		t.Errorf("games_started_total = %v, want scrabble_en:3 scrabble_ru:1", started)
 	}
-	if abandoned := counterByAttr(t, rm, "games_abandoned_total", "variant"); abandoned["erudit_ru"] != 1 {
-		t.Errorf("games_abandoned_total = %v, want erudit_ru:1", abandoned)
+	// The vs_ai attribute splits AI from human games for the per-kind Grafana panels.
+	if byKind := counterByAttr(t, rm, "games_started_total", "vs_ai"); byKind["false"] != 3 || byKind["true"] != 1 {
+		t.Errorf("games_started_total by vs_ai = %v, want false:3 true:1", byKind)
+	}
+	if abandoned := counterByAttr(t, rm, "games_abandoned_total", "vs_ai"); abandoned["false"] != 1 || abandoned["true"] != 1 {
+		t.Errorf("games_abandoned_total by vs_ai = %v, want false:1 true:1", abandoned)
 	}
 	if c := histogramCount(t, rm, "game_replay_duration"); c != 1 {
 		t.Errorf("game_replay_duration observations = %d, want 1", c)
@@ -78,7 +84,7 @@ func counterByAttr(t *testing.T, rm metricdata.ResourceMetrics, name, attr strin
 			}
 			for _, dp := range sum.DataPoints {
 				v, _ := dp.Attributes.Value(attribute.Key(attr))
-				out[v.AsString()] += dp.Value
+				out[v.Emit()] += dp.Value // Emit renders any attribute type (string or bool) to a key
 			}
 		}
 	}