[namanjain24-sudo]

The coordinators start a language runtime with subprocess.Popen and leave it in the supervisor's own
process group, so stopping the task signals the runtime alone. Anything the task started — a CLI spawned
from a TypeScript handler, for instance — is re-parented to init and keeps running alongside the next try,
and holds the runtime's event loop open until the SIGKILL escalation fires after killed_task_cleanup_time.

Python tasks stopped leaking this way in #65505: the task process runs in its own process group so the
supervisor can signal the whole group. WatchedSubprocess._signal_subprocess already does that with
os.killpg whenever new_process_group was recorded at start time, so the runtime only needs the same
treatment — process_group=0 on the Popen, and the flag set on the subprocess object.

This is direction 1 of the two the issue lists. It fixes every path that stops the task, since they all go
through _signal_subprocess: clearing a running task, execution_timeout, repeated heartbeat failures and
task-success overtime.

process_group is POSIX-only, which matches the rest of this machinery — the Python path already calls
os.posix_spawn(..., setpgroup=0) and os.fork() + os.setpgid unconditionally.

closes: #75533

Testing

Checked the real behaviour rather than only the call, with a runtime that spawns a child the way the
issue's handler does:

WITHOUT process_group (old): own_pgid=False  grandchild_alive_after_stop=True
WITH    process_group=0 (fix): own_pgid=True  grandchild_alive_after_stop=False

• New test asserts the runtime is started with its own process group and that the subprocess records it, so
  _signal_subprocess takes the killpg path. It fails without the change (KeyError: 'process_group').
• task-sdk/tests/task_sdk/coordinators/ — 475 passed.
• task-sdk/tests/task_sdk/execution_time/test_supervisor.py — 374 passed, 1 skipped.
• breeze run mypy task-sdk/src/airflow/sdk/coordinators/_subprocess.py — clean.

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[uranusjr]

#75707 is more progressed.