feat(gateway): unsupported-engine telemetry beacon + Grafana counter

The index.html boot guard now fires a fire-and-forget beacon (POST /telemetry/unsupported)
when it turns a client away on the unsupported-engine screen, so the owner can see — on the
Users dashboard beside "app opens" — how many real clients hit it and on which engines.

- Client: navigator.sendBeacon (fetch fallback) with a localStorage dedup keyed by app version
  + reason + Chromium, so a user reopening the app is one report, not ten.
- Gateway: a new unauthenticated POST /telemetry/unsupported handler (the client never booted,
  so it carries no session), per-IP public-limited and body-capped, mirroring the export-download
  route. It folds the beacon into the OTel counter unsupported_engine_total {reason =
  no_bigint/no_proxy/boot_error/other, chromium}, with reason allow-listed and the Chromium major
  reduced to a bounded range (normalizeUnsupported) so a spoofed beacon cannot inflate the metric
  cardinality; the full user agent is logged, not labelled.
- Caddy: /telemetry/* added to the @gateway matcher (else it falls to the landing catch-all).
- Grafana: two panels on the Scrabble — Users dashboard (by reason, by Chromium major).
- Docs: ARCHITECTURE.md §11.

Tests: recordUnsupportedEngine (metric split), normalizeUnsupported (cardinality bounding), and
the handler route end to end (204 / 405 / counter). go build+vet+test and gofmt clean; ui
check/build/e2e green; the client beacon + dedup verified against a forced hard-gate (BigInt
removed) — one POST, deduped on reopen, correct reason/chromium/version labels.

gateway/internal/connectsrv/server.go

@@ -15,6 +15,7 @@ import (
 	"io"
 	"net"
 	"net/http"
+	"strconv"
 	"strings"
 	"time"
 
@@ -197,6 +198,9 @@ func (s *Server) HTTPHandler() http.Handler {
 	mux.Handle("/dl/", s.exportDownloadHandler())
 	// The client posts its local-move-preview adoption telemetry here (session-gated).
 	mux.Handle("/metrics/local-eval", s.localEvalMetricsHandler())
+	// The index.html boot guard beacons here when it turns a client away on the unsupported-engine
+	// screen (the app cannot run). Unauthenticated — the client never booted — but rate-limited.
+	mux.Handle("/telemetry/unsupported", s.unsupportedEngineHandler())
 	// The embedded UI: the game SPA under /app/ (web), /telegram/ (the Telegram Mini
 	// App) and /vk/ (the VK Mini App) — the single-origin model (docs/ARCHITECTURE.md
 	// §13). All sit below the h2c wrap so the Connect edge (a more specific prefix) keeps
@@ -582,6 +586,76 @@ func clampReport(r *localEvalReport) {
 	clamp(&r.PreviewNetwork)
 }
 
+// unsupportedEngineBeacon is the small fire-and-forget report the index.html boot guard sends when
+// it turns a client away on the unsupported-engine screen (no BigInt/Proxy, or an uncaught boot
+// error). It is deduped client-side (one per device / app version / reason).
+type unsupportedEngineBeacon struct {
+	Reason   string `json:"reason"`
+	Chromium string `json:"chromium"`
+	Version  string `json:"version"`
+	UA       string `json:"ua"`
+}
+
+// unsupportedEngineHandler folds one unsupported-engine beacon into the edge counter. It is
+// unauthenticated (the client never booted, so it carries no session) but per-IP rate-limited with
+// the public limiter and body-capped. reason and the Chromium major are reduced to bounded label
+// sets (normalizeUnsupported) so a spoofed beacon cannot inflate the metric cardinality; the full
+// user agent is logged, not labelled. Only POST; the reply is always 204.
+func (s *Server) unsupportedEngineHandler() http.Handler {
+	return http.HandlerFunc(func(w http.ResponseWriter, r *http.Request) {
+		if r.Method != http.MethodPost {
+			http.Error(w, "method not allowed", http.StatusMethodNotAllowed)
+			return
+		}
+		ip := peerIP(r.RemoteAddr, r.Header)
+		if !s.limiter.Allow("public:"+ip, s.publicPolicy) {
+			s.noteRateLimited(r.Context(), classPublic, ip, "unsupported")
+			http.Error(w, "rate limited", http.StatusTooManyRequests)
+			return
+		}
+		var b unsupportedEngineBeacon
+		if err := json.NewDecoder(io.LimitReader(r.Body, 2048)).Decode(&b); err != nil {
+			http.Error(w, "bad request", http.StatusBadRequest)
+			return
+		}
+		reason, chromium := normalizeUnsupported(b.Reason, b.Chromium)
+		s.metrics.recordUnsupportedEngine(r.Context(), reason, chromium)
+		s.log.Info("unsupported engine",
+			zap.String("reason", reason),
+			zap.String("chromium", chromium),
+			zap.String("app_version", truncate(b.Version, 40)),
+			zap.String("user_agent", truncate(b.UA, 400)),
+		)
+		w.WriteHeader(http.StatusNoContent)
+	})
+}
+
+// normalizeUnsupported reduces a beacon's reason and Chromium fields to bounded label values, so a
+// spoofed beacon cannot explode the metric cardinality: reason is allow-listed, and Chromium is
+// parsed as a major version kept only within a plausible range, otherwise "other".
+func normalizeUnsupported(reason, chromium string) (string, string) {
+	switch reason {
+	case "no_bigint", "no_proxy", "boot_error":
+		// a recognised reason — keep as-is
+	default:
+		reason = "other"
+	}
+	major := "other"
+	if n, err := strconv.Atoi(strings.TrimSpace(chromium)); err == nil && n >= 1 && n <= 199 {
+		major = strconv.Itoa(n)
+	}
+	return reason, major
+}
+
+// truncate bounds a logged, client-supplied string to n bytes (a spoofed beacon field is not
+// trusted to be small).
+func truncate(s string, n int) string {
+	if len(s) > n {
+		return s[:n]
+	}
+	return s
+}
+
 // resolve extracts and resolves the Authorization bearer token to an account id
 // and its guest flag, returning a Connect Unauthenticated error when it is missing
 // or unknown.