Adjust deprecation message

homeassistant/helpers/deprecation.py

@@ -149,12 +149,14 @@ def deprecate_hass_binding[**_P, _T](
             from homeassistant.core import HomeAssistant  # noqa: PLC0415
 
             if isinstance(args[0], HomeAssistant):
-                _print_deprecation_warning(
-                    func,
-                    "without hass",
+                _print_deprecation_warning_internal(
+                    "hass",
+                    func.__module__,
+                    f"{func.__name__} without hass argument",
                     "argument",
-                    "called with hass as the first argument",
+                    f"passed to {func.__name__}",
                     breaks_in_ha_version,
+                    log_when_no_integration_is_found=True,
                 )
                 args = args[1:]  # type: ignore[assignment]
             return func(*args, **kwargs)

tests/helpers/test_service.py

@@ -1712,8 +1712,9 @@ async def test_register_admin_service_return_response(
 
 
 _DEPRECATED_VERIFY_DOMAIN_CONTROL_MESSAGE = (
-    "verify_domain_control is a deprecated argument which will be removed"
-    " in HA Core 2026.2. Use without hass instead"
+    "The deprecated argument hass was passed to verify_domain_control. It will be"
+    " removed in HA Core 2026.2. Use verify_domain_control without hass argument"
+    " instead"
 )