feat(sse): heal a stalled SSE stream with a heartbeat + client watchdog

An EventSource that stops delivering does not always error. A proxy that
idle-closed the connection, a laptop resumed from sleep, a tailnet reconnect:
`onerror` never fires, the header dot stays green, and every SSE-driven surface
(tab status dots, sessions created on another device, renames) freezes until the
user reloads. Nothing on the client tracked stream liveness at all.

The server already wrote a keepalive every 15s, but as an SSE `:keepalive`
COMMENT, and comments are invisible to `EventSource` by spec, so there was
nothing a client could observe.

Server:
- `sse:heartbeat` under a new Transport category in the event registry
  (155 constants now, both counts updated).
- `cleanupDeadClients()` writes that named frame (`{"t":<epoch ms>}`) instead of
  the comment. Interval, tunnel padding and dead-socket eviction are unchanged.
  The write stays per-client rather than going through `broadcast()`: the frame
  carries no session data, so it needs no multi-user owner routing.

Client:
- `computeSseStale()` in constants.js, a pure policy beside
  `computeConnectionLossUi`. Stale only when the transport believes it is
  `connected`, the device is online, and no frame has arrived for 45s (three
  missed heartbeats). The `connected`-only guard is also the loop breaker: a
  forced reconnect leaves that state immediately, so the watchdog cannot re-fire
  while one is in flight.
- The liveness stamp is applied inside `addListener` itself, so the
  `_SSE_HANDLER_MAP` wrappers and the directly-registered listeners all feed it
  from one place instead of three that can drift. The heartbeat's own listener
  is a no-op that exists only to be registered, since `EventSource` drops named
  events nobody listens for.
- A 5s watchdog forces `connectSSE()` when the policy says stale, and is cleared
  at the top of `connectSSE()` and nowhere else (its only teardown path).
  Recovery needs no new sync path: the reconnect re-runs `handleInit`, which
  already rebuilds from the server. `visibilitychange` -> visible checks too,
  riding the existing listener, since a background tab's timers are throttled
  and a wake is exactly when a stream comes back zombie.
- The forced reconnect logs one diagnostic line: if a middlebox ever strips or
  delays heartbeats, the failure mode is "silently reconnects every 45s", which
  is undebuggable from a field report without it.

Tests: `test/sse-staleness.test.ts` (node VM over constants.js, threshold
boundaries and every not-stale guard) and `test/sse-heartbeat.test.ts` (drives
`cleanupDeadClients()` with fake replies: named frame not a comment, parseable
payload, padding only with a tunnel, dead clients still evicted).

Verified end to end on an isolated instance: with the stream closed client-side
(no `onerror`), a rename sticks, an out-of-band session stays invisible, then
the watchdog reconnects on its own and it appears without a reload.

Event names are part of the stable API contract, so this is a MINOR bump.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

docs/api-reference.md

@@ -534,6 +534,29 @@ the stable contract — event names are not renamed without a major bump. An
 optional `?sessions=<id,...>` filter suppresses only the high-volume terminal
 stream; lifecycle/metadata events are delivered to all clients regardless.
 
+### `sse:heartbeat` (liveness)
+
+Every 15s the server writes a `sse:heartbeat` frame to every connected client:
+
+```
+event: sse:heartbeat
+data: {"t":1755100000000}
+```
+
+`t` is the server's epoch-ms timestamp at write time. The frame carries no
+application state and can be ignored for correctness. It exists so a client can
+tell a live stream from a dead one: an `EventSource` whose connection has been
+idle-closed by a proxy (or that resumed from sleep on a stale socket) keeps
+delivering nothing without ever firing `onerror`. Clients that care should treat
+silence longer than about three intervals as a dead stream and reconnect, which
+is what the bundled frontend does.
+
+This replaced a `:keepalive` SSE **comment**, which served the same
+proxy-flushing purpose but is invisible to `EventSource` by spec and so could
+never be observed by a client. Consumers written against the old behavior are
+unaffected: `EventSource` dispatches only events that have a registered
+listener, so an unknown event name is dropped.
+
 ## Consuming from JavaScript
 
 The bundled frontend reads responses through `_apiJson()`