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.go

@@ -22,6 +22,7 @@ const meterName = "scrabble/backend/game"
 type gameMetrics struct {
 	replay    metric.Float64Histogram
 	validate  metric.Float64Histogram
+	moveDur   metric.Float64Histogram
 	started   metric.Int64Counter
 	abandoned metric.Int64Counter
 }
@@ -39,6 +40,7 @@ func newGameMetrics(meter metric.Meter) *gameMetrics {
 	return &gameMetrics{
 		replay:    histogram(meter, "game_replay_duration", "Seconds to rebuild a live game from its journal on a cache miss."),
 		validate:  histogram(meter, "game_move_validate_duration", "Seconds to validate and score a tentative play (EvaluatePlay)."),
+		moveDur:   histogram(meter, "game_move_duration", "Seconds a seat spent on a committed move (play/pass/exchange), by variant and phase. Aggregates all seats including robots; per-human analysis lives in the admin console."),
 		started:   counter(meter, "games_started_total", "Games created and started."),
 		abandoned: counter(meter, "games_abandoned_total", "Player seats dropped by the turn-timeout sweeper."),
 	}
@@ -75,6 +77,30 @@ func (m *gameMetrics) recordValidate(ctx context.Context, v engine.Variant, star
 	m.validate.Record(ctx, time.Since(start).Seconds(), variantAttr(v))
 }
 
+// recordMoveDuration records how long a seat spent on a committed move, attributed by
+// variant and the game phase derived from moveCount. A non-positive duration (a clock
+// skew or a move with no recorded turn start) is dropped.
+func (m *gameMetrics) recordMoveDuration(ctx context.Context, v engine.Variant, moveCount int, d time.Duration) {
+	if d <= 0 {
+		return
+	}
+	m.moveDur.Record(ctx, d.Seconds(),
+		metric.WithAttributes(attribute.String("variant", v.String()), attribute.String("phase", phaseOf(moveCount))))
+}
+
+// phaseOf buckets a move ordinal into the game phase used as a metric attribute. The
+// thresholds reflect a typical ~28-move game (docs/ARCHITECTURE.md §7).
+func phaseOf(moveCount int) string {
+	switch {
+	case moveCount <= 8:
+		return "opening"
+	case moveCount <= 20:
+		return "middle"
+	default:
+		return "endgame"
+	}
+}
+
 // recordStarted counts one started game of variant.
 func (m *gameMetrics) recordStarted(ctx context.Context, v engine.Variant) {
 	m.started.Add(ctx, 1, variantAttr(v))