fix(api): reserve db pool for serving readbacks

apps/api/tests/test_runtime_bootstrap_guards.py

@@ -257,6 +257,51 @@ def test_api_lifespan_closes_worker_redis_pool_after_signal_worker() -> None:
     assert source.index("close_worker_redis_pool") < source.index("close_redis_pool")
 
 
+def test_api_background_tasks_default_off_when_db_pool_has_no_spare_slot(monkeypatch) -> None:
+    from src import main as api_main
+
+    monkeypatch.delenv(api_main.API_BACKGROUND_TASKS_ENV, raising=False)
+    monkeypatch.setattr(api_main.settings, "DATABASE_POOL_SIZE", 1)
+    monkeypatch.setattr(api_main.settings, "DATABASE_MAX_OVERFLOW", 0)
+
+    assert api_main.should_start_api_background_tasks() is False
+
+
+def test_api_background_tasks_default_on_when_db_pool_has_spare_slot(monkeypatch) -> None:
+    from src import main as api_main
+
+    monkeypatch.delenv(api_main.API_BACKGROUND_TASKS_ENV, raising=False)
+    monkeypatch.setattr(api_main.settings, "DATABASE_POOL_SIZE", 2)
+    monkeypatch.setattr(api_main.settings, "DATABASE_MAX_OVERFLOW", 0)
+
+    assert api_main.should_start_api_background_tasks() is True
+
+
+def test_api_background_tasks_env_override_controls_serving_budget(monkeypatch) -> None:
+    from src import main as api_main
+
+    monkeypatch.setattr(api_main.settings, "DATABASE_POOL_SIZE", 1)
+    monkeypatch.setattr(api_main.settings, "DATABASE_MAX_OVERFLOW", 0)
+
+    monkeypatch.setenv(api_main.API_BACKGROUND_TASKS_ENV, "true")
+    assert api_main.should_start_api_background_tasks() is True
+
+    monkeypatch.setenv(api_main.API_BACKGROUND_TASKS_ENV, "false")
+    assert api_main.should_start_api_background_tasks() is False
+
+
+def test_api_lifespan_routes_background_loops_through_serving_budget_gate() -> None:
+    import inspect
+
+    from src import main as api_main
+
+    source = inspect.getsource(api_main.lifespan)
+    assert "schedule_api_background_task(run_incident_analysis_sweeper())" in source
+    assert "schedule_api_background_task(run_km_backfill_reconciler_loop())" in source
+    assert "signal_worker_skipped" in source
+    assert "platform_worker_skipped" in source
+
+
 def test_init_db_backfills_all_optional_knowledge_read_columns() -> None:
     import inspect