Stage 12: observability & performance (OTel/OTLP, domain metrics, guest GC)

- pkg/telemetry: shared OTel provider bootstrap (none/stdout/otlp + W3C
  propagators + Go runtime metrics); backend/internal/telemetry becomes a thin
  facade keeping its gin middleware.
- Telemetry parity: gateway and the Telegram connector gain telemetry runtimes
  and config (GATEWAY_/TELEGRAM_ SERVICE_NAME + OTEL_*); otelgrpc instruments the
  backend push server, the gateway's backend+connector clients and the connector
  server. Default exporter stays none (collector/dashboards are Stage 14).
- Operational metrics (variant attribute on game-scoped ones): game_replay_duration,
  game_move_validate_duration, games_started_total, games_abandoned_total,
  game_cache_active, chat_messages_total{kind}, gateway edge_request_duration.
  Wired via the SetMetrics setter pattern (default no-op meter).
- TODO-3: account.GuestReaper deletes guests with no game seat past
  BACKEND_GUEST_RETENTION (default 30d, swept every BACKEND_GUEST_REAP_INTERVAL).
- Tests: pkg/telemetry exporter selection; game/social/edge metric recording via
  a manual reader; config (otlp accepted, guest knobs); inttest guest reaper.
- Docs: PLAN.md re-scopes Stage 12 and adds Stage 13 (alphabet-on-wire) + Stage 14
  (CI/deploy) with the agreed dictionary-versioning resolution; ARCHITECTURE 11/13,
  TESTING, the three READMEs and FUNCTIONAL(+ru) updated.

backend/internal/game/metrics_test.go

@@ -0,0 +1,95 @@
+package game
+
+import (
+	"context"
+	"testing"
+	"time"
+
+	"go.opentelemetry.io/otel/attribute"
+	sdkmetric "go.opentelemetry.io/otel/sdk/metric"
+	"go.opentelemetry.io/otel/sdk/metric/metricdata"
+
+	"scrabble/backend/internal/engine"
+)
+
+// TestGameMetrics records each game instrument through a manual reader and asserts
+// the counters carry the right "variant" attribute and the histograms observe.
+func TestGameMetrics(t *testing.T) {
+	ctx := context.Background()
+	reader := sdkmetric.NewManualReader()
+	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.recordReplay(ctx, engine.VariantEnglish, time.Now().Add(-time.Millisecond))
+	m.recordValidate(ctx, engine.VariantRussianScrabble, time.Now().Add(-time.Millisecond))
+
+	var rm metricdata.ResourceMetrics
+	if err := reader.Collect(ctx, &rm); err != nil {
+		t.Fatalf("collect: %v", err)
+	}
+
+	started := counterByAttr(t, rm, "games_started_total", "variant")
+	if started["english"] != 2 || started["russian_scrabble"] != 1 {
+		t.Errorf("games_started_total = %v, want english:2 russian_scrabble:1", started)
+	}
+	if abandoned := counterByAttr(t, rm, "games_abandoned_total", "variant"); abandoned["erudit"] != 1 {
+		t.Errorf("games_abandoned_total = %v, want erudit:1", abandoned)
+	}
+	if c := histogramCount(t, rm, "game_replay_duration"); c != 1 {
+		t.Errorf("game_replay_duration observations = %d, want 1", c)
+	}
+	if c := histogramCount(t, rm, "game_move_validate_duration"); c != 1 {
+		t.Errorf("game_move_validate_duration observations = %d, want 1", c)
+	}
+}
+
+// counterByAttr sums the int64 counter named name, grouped by the value of the
+// attribute key attr.
+func counterByAttr(t *testing.T, rm metricdata.ResourceMetrics, name, attr string) map[string]int64 {
+	t.Helper()
+	out := map[string]int64{}
+	for _, sm := range rm.ScopeMetrics {
+		for _, md := range sm.Metrics {
+			if md.Name != name {
+				continue
+			}
+			sum, ok := md.Data.(metricdata.Sum[int64])
+			if !ok {
+				t.Fatalf("%s is not an int64 sum", name)
+			}
+			for _, dp := range sum.DataPoints {
+				v, _ := dp.Attributes.Value(attribute.Key(attr))
+				out[v.AsString()] += dp.Value
+			}
+		}
+	}
+	return out
+}
+
+// histogramCount returns the total observation count of the float64 histogram
+// named name.
+func histogramCount(t *testing.T, rm metricdata.ResourceMetrics, name string) uint64 {
+	t.Helper()
+	for _, sm := range rm.ScopeMetrics {
+		for _, md := range sm.Metrics {
+			if md.Name != name {
+				continue
+			}
+			h, ok := md.Data.(metricdata.Histogram[float64])
+			if !ok {
+				t.Fatalf("%s is not a float64 histogram", name)
+			}
+			var n uint64
+			for _, dp := range h.DataPoints {
+				n += dp.Count
+			}
+			return n
+		}
+	}
+	t.Fatalf("%s not found", name)
+	return 0
+}