fix(net): detect a silently-dead live stream via a heartbeat watchdog

An idle live stream whose connection dies without an error (airplane mode
cutting the radio) left the net-state machine stuck "online": the streaming
fetch neither errored nor delivered, no unary call was made, and the OS
`navigator` offline hint is unreliable in the Telegram/VK WebViews — so the
"Connecting…"/offline state only surfaced on the next foreground resync, not
while idle.

The gateway already pushes a keep-alive `heartbeat` every 10s, so add a
client-side watchdog (streamwatchdog.ts) that resets on every delivered event
and, after ~25s of silence, treats the stream as dropped (reportOffline +
reconnect). It is background-aware (paused while suspended) so a throttled
foreground return does not false-trip. The mock client mirrors the heartbeat
so an idle e2e session stays online.

ui/src/lib/streamwatchdog.ts

@@ -0,0 +1,63 @@
+// A liveness watchdog for the live event stream. The gateway pushes a `heartbeat` event on a
+// fixed cadence (GATEWAY_PUSH_HEARTBEAT_INTERVAL, default 10 s), so a healthy stream delivers at
+// least one event well inside the timeout even when the game itself is idle. A network that dies
+// silently — e.g. airplane mode cutting the radio — leaves the streaming fetch neither erroring
+// nor delivering; without this watchdog the machine would stay "online" until the next active
+// call fails (often only on a foreground resync). The watchdog resets on every delivered event
+// and fires onDead once the stream has been silent for the whole timeout, so the app can report
+// the drop and reconnect.
+
+/** StreamWatchdog is the control surface returned by {@link createStreamWatchdog}. */
+export interface StreamWatchdog {
+  /** reset (re)starts the countdown; call on stream open and on every delivered event. It also
+   *  clears a prior pause, so a reopen after a suspend resumes watching. */
+  reset(): void;
+  /** pause stops the countdown while the app is backgrounded (timers are throttled while hidden,
+   *  and a suspended stream legitimately delivers nothing — neither should trip a false drop). */
+  pause(): void;
+  /** resume restarts the countdown after a pause (on returning to the foreground). */
+  resume(): void;
+  /** clear stops the countdown without re-arming; call when the stream is closed or has errored. */
+  clear(): void;
+}
+
+/**
+ * createStreamWatchdog builds a watchdog that calls onDead once no reset has happened for
+ * timeoutMs. timeoutMs must exceed the server heartbeat interval plus proxy/jitter slack, or a
+ * healthy but idle stream would trip it.
+ */
+export function createStreamWatchdog(opts: { timeoutMs: number; onDead: () => void }): StreamWatchdog {
+  let timer: ReturnType<typeof setTimeout> | null = null;
+  let paused = false;
+
+  function stop(): void {
+    if (timer !== null) {
+      clearTimeout(timer);
+      timer = null;
+    }
+  }
+  function arm(): void {
+    stop();
+    timer = setTimeout(opts.onDead, opts.timeoutMs);
+  }
+
+  return {
+    reset(): void {
+      paused = false;
+      arm();
+    },
+    pause(): void {
+      paused = true;
+      stop();
+    },
+    resume(): void {
+      if (paused) {
+        paused = false;
+        arm();
+      }
+    },
+    clear(): void {
+      stop();
+    },
+  };
+}