feat(telemetry): local move-preview adoption metrics (Phase 4)

Measure uptake of the client-side local move-preview accelerator (§5) so
adoption can be watched before defaulting it on: app cold starts, dictionary
loads by result (fetched / cache_hit / miss) and move previews by path
(local / network — the backend load shed).

A small best-effort client beacon (POST /metrics/local-eval, session-gated)
batches counter deltas and posts them on a 60s timer and when the app is
backgrounded — never on the gameplay path: the in-app counters are plain
in-memory increments, only the periodic flush touches the network and it is
fire-and-forget. The gateway folds each batch into three OTel counters
(local_eval_cold_start_total, local_eval_dict_load_total,
local_eval_preview_total), clamped against a spoofed inflation.

- gateway: counters + recordLocalEval + session-gated /metrics/local-eval handler
- ui: localeval-metrics accumulator/beacon; hooks in the dict loader, in
  Game.recompute and in bootstrap (skipped under the mock harness)
- caddy: route /metrics/* to the gateway
- docs: ARCHITECTURE §11; Grafana "Scrabble — Users" dashboard panels

gateway/internal/connectsrv/metrics.go

@@ -28,6 +28,10 @@ type serverMetrics struct {
 	rateLimited metric.Int64Counter
 	banned      metric.Int64Counter
 	active      *activeUsers
+	// Client-reported local move-preview adoption (see localEvalMetricsHandler).
+	localColdStart metric.Int64Counter
+	localDictLoad  metric.Int64Counter
+	localPreview   metric.Int64Counter
 }
 
 // newServerMetrics builds the instruments on meter (nil selects a no-op meter),
@@ -54,7 +58,12 @@ func newServerMetrics(meter metric.Meter) *serverMetrics {
 	if err != nil {
 		b, _ = noop.NewMeterProvider().Meter(meterName).Int64Counter("gateway_abuse_banned_total")
 	}
-	m := &serverMetrics{edge: h, rateLimited: c, banned: b, active: newActiveUsers()}
+	m := &serverMetrics{
+		edge: h, rateLimited: c, banned: b, active: newActiveUsers(),
+		localColdStart: counterOf(meter, "local_eval_cold_start_total", "App cold starts reported by clients — the denominator for local-move-preview adoption."),
+		localDictLoad:  counterOf(meter, "local_eval_dict_load_total", "Client dictionary loads for the local move preview, by result (fetched, cache_hit or miss)."),
+		localPreview:   counterOf(meter, "local_eval_preview_total", "Client move previews, by path (local on-device, or network fallback)."),
+	}
 
 	gauge, err := meter.Int64ObservableGauge("active_users",
 		metric.WithDescription("Distinct accounts that performed an authenticated action within the window (in-memory, single gateway instance)."))
@@ -98,3 +107,40 @@ func (m *serverMetrics) recordRateLimited(ctx context.Context, class string) {
 func (m *serverMetrics) recordBan(ctx context.Context, reason string) {
 	m.banned.Add(ctx, 1, metric.WithAttributes(attribute.String("reason", reason)))
 }
+
+// localEvalReport is the client-reported local move-preview telemetry batch — deltas since
+// the client's previous report. It backs the adoption dashboard: app cold starts vs cached
+// dictionaries vs on-device previews.
+type localEvalReport struct {
+	ColdStart      int `json:"cold_start"`
+	DictFetched    int `json:"dict_fetched"`
+	DictCacheHit   int `json:"dict_cache_hit"`
+	DictMiss       int `json:"dict_miss"`
+	PreviewLocal   int `json:"preview_local"`
+	PreviewNetwork int `json:"preview_network"`
+}
+
+// recordLocalEval folds one client report into the edge's local-eval counters.
+func (m *serverMetrics) recordLocalEval(ctx context.Context, r localEvalReport) {
+	add := func(c metric.Int64Counter, n int, opts ...metric.AddOption) {
+		if n > 0 {
+			c.Add(ctx, int64(n), opts...)
+		}
+	}
+	add(m.localColdStart, r.ColdStart)
+	add(m.localDictLoad, r.DictFetched, metric.WithAttributes(attribute.String("result", "fetched")))
+	add(m.localDictLoad, r.DictCacheHit, metric.WithAttributes(attribute.String("result", "cache_hit")))
+	add(m.localDictLoad, r.DictMiss, metric.WithAttributes(attribute.String("result", "miss")))
+	add(m.localPreview, r.PreviewLocal, metric.WithAttributes(attribute.String("path", "local")))
+	add(m.localPreview, r.PreviewNetwork, metric.WithAttributes(attribute.String("path", "network")))
+}
+
+// counterOf builds an Int64Counter on meter, falling back to a no-op on the rare
+// construction error so metrics never fail startup.
+func counterOf(meter metric.Meter, name, desc string) metric.Int64Counter {
+	c, err := meter.Int64Counter(name, metric.WithDescription(desc))
+	if err != nil {
+		c, _ = noop.NewMeterProvider().Meter(meterName).Int64Counter(name)
+	}
+	return c
+}