Problem

#44183: when a Mac sleeps with Hermes Desktop open, the WS connection drops and the gateway parks the session behind the 20s orphan-reap grace (HERMES_TUI_WS_ORPHAN_REAP_GRACE_S). After any sleep longer than the grace, the session is reaped at the instant of wake — before the Desktop can reconnect or session.resume — so actions on the open chat 404 with "session not found".

Root cause

threading.Timer's wait elapses in wall-clock time on macOS: CPython's lock wait uses pthread_cond_timedwait with a CLOCK_REALTIME deadline because macOS has no pthread_condattr_setclock. The wall clock keeps running while the host sleeps, so the timer's deadline expires during the sleep and _reap fires immediately at wake — the reap always wins the race against the Desktop's reconnect.

time.monotonic() (mach_absolute_time on macOS, CLOCK_MONOTONIC on Linux) does not advance during sleep, which gives a clean way to distinguish "20s of awake time elapsed" from "the host slept through the wait".

Fix

_schedule_ws_orphan_reap records a time.monotonic() deadline at schedule time. When _reap fires, it first checks the monotonic clock: if more than a small slack (0.5s) of the grace is still unelapsed in awake time, the host slept through the wait — re-arm a timer for the remainder instead of reaping. The Desktop therefore gets the full grace of awake time after wake to re-bind a transport (which cancels the reap exactly as before).

• The default grace stays 20s, so genuinely orphaned sessions (browser refresh, the feat(dashboard): always enable embedded chat; remove dashboard --tui flag #38591 leak this reaper exists for) are reaped on the same schedule as today.
• Repeated sleep cycles just keep re-arming until 20 cumulative seconds of awake time pass without a reconnect.
• On platforms where the timer wait already pauses during suspend, the monotonic check is a no-op (fires with remaining <= 0), so behaviour is unchanged.
• The 0.5s slack absorbs timer jitter and forward NTP steps without re-arming spuriously; normal (no-sleep) firings have remaining <= 0.

Related: #44102 re-arms this same timer while a detached session is mid-turn — independent condition, trivially composable if both land.

Tests

• test_ws_orphan_reap_rearms_after_system_sleep — timer fires with only 2s of 20s elapsed on a fake monotonic clock → spared and re-armed for 18s; the re-armed timer then reaps after a full awake remainder.
• test_ws_orphan_reap_rearm_spares_post_wake_reconnect — Desktop re-binds a live transport within the post-wake remainder → reap is a no-op and the chain stops.

pytest tests/test_tui_gateway_server.py: 258 passed, 1 failed — test_browser_manage_connect_default_local_reports_launch_hint, which also fails on clean main (85503dc) and is unrelated.

Fixes #44183

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