feat(gateway): unsigned gateway.heartbeat keeps Safari push streams alive

Browser fetch-streaming layers close response bodies they consider
idle after roughly 15-30 s without incoming bytes. Safari is the
most aggressive, but the symptom matters everywhere: a quiet
SubscribeEvents stream (lobby, between turns, mailbox empty) gets
torn down by the browser, the EventStream singleton reconnects with
backoff, and any push event that fires inside the reconnect window
is lost because `push.Hub` queues are not persisted across
subscription closes. The user-visible failure mode is the
intermittent "Fetch API cannot load … due to access control checks"
console error (a misleading WebKit symptom — CORS headers are
actually present) plus missed turn-ready / mail-received toasts.

Server-side fix: a silence-based heartbeat at the
`authenticatedPushStreamService` wrapper layer. After the signed
`gateway.server_time` bootstrap event, gateway wraps the bound
stream with `heartbeatingStream`. Every tail Send (fan-out, future
variants) resets the silence timer; when the timer elapses, a
goroutine emits `gateway.heartbeat` with only `EventType` set —
everything else stays at proto3 defaults, so the wire frame is
~45 bytes amortised. A `sendMu` serialises the heartbeat goroutine
with tail Sends because grpc.ServerStream.Send is not goroutine-safe.

The heartbeat is intentionally UNSIGNED: heartbeats carry no
payload, dispatch to no handler on the client, and an injected
heartbeat trivially causes no user-visible state change. TLS still
protects the wire and real events keep the signed envelope
unchanged. Documented in `docs/ARCHITECTURE.md` § 15 alongside the
per-scale bandwidth projection (100…100 000 clients × 15…60 s).

Config: new `GATEWAY_PUSH_HEARTBEAT_INTERVAL` (default `15s`,
`0s` disables). Telemetry: new
`gateway.push.heartbeats_sent{outcome}` counter so operators can
budget bandwidth and spot a sudden `outcome=error` bump as an
upstream-failing-before-flush signal.

Client (`ui/frontend/src/api/events.svelte.ts`): early `continue`
on `event.eventType === "gateway.heartbeat"` before `verifyEvent`,
`verifyPayloadHash`, or dispatch — empty signature would otherwise
trip SignatureError and reconnect. A leading heartbeat still flips
`connectionStatus` to `connected` and resets backoff, because
receiving one is proof the stream is healthy.

Tests:
- `push_heartbeat_test.go`: unit tests for the wrapper — zero
  interval returns nil, heartbeat fires after silence, real Send
  resets the timer, Stop / context-cancel halt the goroutine,
  Send errors propagate.
- `server_test.go`: integration tests through the full gateway
  pipeline — heartbeat fires after the configured silence window,
  zero interval keeps the stream silent.
- `config_test.go`: default applied, env-override parsed,
  negative value rejected.
- `events.test.ts`: heartbeat skipped before verification + not
  dispatched to handlers; leading heartbeat still flips
  `connectionStatus` to `connected`.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

docs/FUNCTIONAL.md

@@ -820,6 +820,18 @@ internal hub. The first frame the client receives is a
 gateway-signed bootstrap event carrying the current server time, so
 the client can calibrate its local clock without a separate request.
 
+While the stream is open, gateway tracks a silence timer; if no real
+event has been forwarded for `GATEWAY_PUSH_HEARTBEAT_INTERVAL`
+(default `15s`, `0s` disables), gateway emits an unsigned
+`gateway.heartbeat` event to keep browser fetch-streaming layers
+from closing the response body as idle. Real events reset the
+timer, so on busy streams the heartbeat fires rarely. The UI client
+short-circuits the heartbeat type before signature verification and
+never dispatches it to handlers — see
+[`docs/ARCHITECTURE.md` § 15](ARCHITECTURE.md#15-transport-security-model-gateway-boundary)
+for the wire-cost projection and the security rationale of leaving
+the heartbeat unsigned.
+
 ### 7.3 Backend → gateway control
 
 Backend hosts a single gRPC service `Push.SubscribePush`, consumed