The #4151 focus hook reopened both global sidebar streams on `focus` with a
bare `startGatewaySSE()`. But `startGatewaySSE()` is NOT idempotent — it begins
with an unconditional `stopGatewaySSE()` (sessions.js:3778), which closes the
live gateway EventSource, cancels its poll fallback (`stopGatewayPollFallback`),
and resets `_gatewayProbeInFlight` / `_gatewaySSEWarningShown`.
So on a transient blur shorter than the 1s debounce — where the blur-close
timer is cleared on the following focus and the stream was never torn down —
the focus handler still dropped and reconnected the gateway on every
window-switch, cancelling its fallback and resetting probe/warning state. That
is the exact thrash the debounce exists to prevent, in the multi-window PWA
scenario this PR targets. (`ensureSessionEventsSSE()` is already idempotent via
`if(_sessionEventsSSE) return`, so the session-events stream was unaffected;
only the gateway churned. greptile P1.)
Guard the reopen on the gateway actually being closed: `if(!_gatewaySSE)
startGatewaySSE()`, mirroring the session-events idempotency. A sustained blur
(timer fires → both streams closed) still reopens the gateway on focus; a
transient blur leaves the still-open gateway untouched. Verified with a
blur/focus/timer harness (transient → no teardown/reconnect; sustained → close
then reopen; CLI-disabled → stays closed) and a new regression guard
`test_focus_reopen_does_not_thrash_the_gateway_stream`.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
