Closes#63529
Root cause: GatewayRunner._drain_active_agents only waited on
_running_agents + cron in-flight counts. Desktop/API sessions are
tracked solely inside APIServerAdapter (_inflight_agent_runs +
_active_run_agents), so stop/restart logged active_at_start=0 and
systemd SIGKILL'd mid-tool work.
Fix: APIServerAdapter.active_agent_work_count() plus
GatewayRunner._active_api_run_count() folded into the drain wait,
status updates, timeout result, and shutdown logs — same pattern as
_active_cron_job_count for #60432.
Verification: pytest tests/gateway/test_api_server_active_work_drain.py
tests/gateway/test_cron_active_work_drain.py -q → 19 passed