Stage 17: backend defect fixes (nudge code, TG name, robot names/timing, multi-device push, move-duration metric + admin analytics)

- #3 nudge-on-own-turn: distinct result code nudge_own_turn + i18n (was reused 'not_your_turn')
- #2 sanitize connector registration name to the editable format; Player/Игрок-XXXXX fallback
- #5 variant-aware robot name pools (composed full/colloquial first + surname forms; ru gets <=20% latin)
- #4 move-number-aware robot move timing (early 1-5min -> late 10-90min, skew k=4)
- #7 emit move event to the actor too (multi-device sync); opponent_moved stays in-app only
- #1 live game_move_duration{variant,phase} histogram + admin console per-user min/avg/max columns and an inline-SVG move-time-by-move-number chart (offline from the journal)
- ProvisionRobot bypasses editor name validation (system names like 'Peter J.')

backend/internal/game/metrics_test.go

@@ -26,6 +26,8 @@ func TestGameMetrics(t *testing.T) {
 	m.recordAbandoned(ctx, engine.VariantErudit)
 	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)
+	m.recordMoveDuration(ctx, engine.VariantEnglish, 3, 0) // non-positive: dropped
 
 	var rm metricdata.ResourceMetrics
 	if err := reader.Collect(ctx, &rm); err != nil {
@@ -45,6 +47,19 @@ func TestGameMetrics(t *testing.T) {
 	if c := histogramCount(t, rm, "game_move_validate_duration"); c != 1 {
 		t.Errorf("game_move_validate_duration observations = %d, want 1", c)
 	}
+	if c := histogramCount(t, rm, "game_move_duration"); c != 1 {
+		t.Errorf("game_move_duration observations = %d, want 1 (zero-duration dropped)", c)
+	}
+}
+
+// TestPhaseOf checks the move-ordinal to phase bucketing.
+func TestPhaseOf(t *testing.T) {
+	cases := map[int]string{1: "opening", 8: "opening", 9: "middle", 20: "middle", 21: "endgame", 50: "endgame"}
+	for mc, want := range cases {
+		if got := phaseOf(mc); got != want {
+			t.Errorf("phaseOf(%d) = %q, want %q", mc, got, want)
+		}
+	}
 }
 
 // counterByAttr sums the int64 counter named name, grouped by the value of the