Scheduler deadlocks in pipe write during task dispatch (LocalExecutor) — runtime variant of #67881

### Under which category would you file this issue? Airflow Core ### Apache Airflow version 3.3.0 ### What happened and how to reproduce it? **Issue Description** The scheduler permanently deadlocks during **normal task dispatch** (not shutdown), blocked in a pipe `write()` to the LocalExecutor's activity queue. All dispatch halts; the SchedulerJob heartbeat stops while the systemd service stays "active". ~10 minutes later, every running task's supervisor kills its task ("Server indicated the task shouldn't be running anymore"), burning retry attempts. This appears to be the **runtime/dispatch-path variant of the shutdown deadlock fixed in #67881** (merged 2026-07-02, not yet released — 3.3.0 still ships the pre-fix `end()` and empty `terminate()`). Occurred **4 times in ~14 hours** on one production host once dispatch volume rose (~150–250 concurrent tasks). Identical signature each time. **Evidence captured mid-deadlock:** - `/proc/<scheduler-pid>/stack` → blocked in `pipe_write` - `/proc/<scheduler-pid>/syscall` → `write(fd=9)`; fd 9 → `pipe:[<inode>]` - Scanning `/proc/*/fd`: the **same pipe inode held (read fd 7 + write fd 9) by the scheduler and every LocalExecutor worker process** - Host healthy: 100+ GB free RAM, idle CPU, no OOM, clean kernel log - One occurrence happened with **zero** api-server errors/timeouts, ruling out API-side causes **Steps to reproduce:** Race condition — probabilistic and load-correlated, so not minimally deterministic, but reliably triggered in our environment within minutes-to-hours: 1. LocalExecutor, `parallelism = 256`, default `max_tis_per_query` (512), PostgreSQL backend 2. Generate dispatch bursts of 150–250 mostly lightweight, long-running tasks (ours poll remote Spark jobs), with tasks completing (returning results) concurrently with new dispatch 3. Scheduler eventually blocks forever in `pipe_write`; heartbeat stops Notably there is no clean load threshold: the same host survived a 30-minute soak at 256 running tasks, the…