fix: make the home location lookup work against Claude

- Send the location question as a user message. A request with only a
  system message has no user content, which endpoints in front of Anthropic
  models reject ("text content blocks must be non-empty").
- Leave unknown fields out of the web search user_location. After a failed
  lookup there is no city or region, and the empty strings made every
  request fail ("user_location.city: String should have at least 1
  character").

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

tests/test_entity.py

@@ -3,14 +3,21 @@
 from unittest.mock import MagicMock
 
 from homeassistant.components import conversation
+from homeassistant.core import Context
 from homeassistant.helpers import llm
 
+from custom_components.openai_compatible.const import (
+    CONF_WEB_SEARCH,
+    CONF_WEB_SEARCH_COUNTRY,
+    CONF_WEB_SEARCH_TIMEZONE,
+    CONF_WEB_SEARCH_USER_LOCATION,
+)
 from custom_components.openai_compatible.entity import (
     _convert_content_to_param,
     _transform_stream,
 )
 
-from . import create_function_tool_call_item
+from . import create_function_tool_call_item, create_message_item
 
 
 async def _stream(events):
@@ -90,3 +97,41 @@ def test_web_search_not_replayed() -> None:
     ]
     assert messages[1]["content"] == "It ended 2 to 2."
     assert messages[2]["call_id"] == "call_1"
+
+
+async def test_web_search_location_leaves_out_empty_fields(
+    hass, mock_config_entry, mock_init_component, mock_create_stream
+) -> None:
+    """Test unknown location fields are left out of the web search tool.
+
+    A failed location lookup stores no city or region; endpoints in front of
+    Anthropic models reject empty strings there.
+    """
+    subentry = next(iter(mock_config_entry.subentries.values()))
+    hass.config_entries.async_update_subentry(
+        mock_config_entry,
+        subentry,
+        data={
+            **subentry.data,
+            CONF_WEB_SEARCH: True,
+            CONF_WEB_SEARCH_USER_LOCATION: True,
+            CONF_WEB_SEARCH_COUNTRY: "DE",
+            CONF_WEB_SEARCH_TIMEZONE: "Europe/Berlin",
+        },
+    )
+    await hass.config_entries.async_reload(mock_config_entry.entry_id)
+    mock_create_stream.return_value = [
+        create_message_item(id="msg_A", text="Hi", output_index=0)
+    ]
+
+    await conversation.async_converse(
+        hass, "hello", None, Context(), agent_id="conversation.openai_conversation"
+    )
+
+    tools = mock_create_stream.mock_calls[0][2]["tools"]
+    web_search = next(tool for tool in tools if tool["type"] == "web_search")
+    assert web_search["user_location"] == {
+        "type": "approximate",
+        "country": "DE",
+        "timezone": "Europe/Berlin",
+    }