The polling heartbeat's pending-update probe treated a stopped updater
(running=False) as "someone else's job" and silently reset its counter,
so a long-poll task that disappears with no reconnect in flight was never
recovered. get_me() on the general request path stays healthy, so neither
PTB's error_callback nor the connectivity probe ever fires — the gateway
keeps running but stops receiving messages indefinitely (#55769).
Detect the stopped-updater case directly in _probe_pending_updates and feed
it into the existing _handle_polling_network_error ladder, debounced over two
consecutive probes so a just-starting updater or the brief stop()->start_polling()
window of an in-flight reconnect never trips it.
The merged CLOSE-WAIT heartbeat (#52744) only probes get_me(), which uses the
general request path and stays healthy while PTB's getUpdates consumer is
silently wedged (updater.running=True but the long-poll task is stuck, observed
on WSL2). DMs then queue in the Bot API and never reach handlers (#42909).
Augment the existing _polling_heartbeat_loop to also probe
get_webhook_info().pending_update_count. After two consecutive probes that see a
non-draining queue while the updater claims to be running, escalate into the
existing _handle_polling_network_error recovery ladder — no new restart
machinery. No-ops in webhook mode, when the updater is not running, or when a
reconnect is already in flight.
Credit to @gazzumatteo, whose PR #42959 identified the pending_update_count
signal as the missing liveness probe. This reuses the existing heartbeat +
recovery path rather than adding a parallel watchdog.
Fixes#42909.
