fix: make the integration work against a Claude proxy

- Treat an empty tool argument string as no parameters instead of raising
  JSONDecodeError; the proxy sends "" for tools like the timer status
  (upstream issue #3).
- Do not replay earlier web searches in the history. The chat log keeps only
  their status, and a search without results makes the model disown the
  answers it based on it and search again (upstream issue #4).
- Look up the home location for web search with the subentry's model instead
  of gpt-4o-mini, and save the options without city/region if the lookup
  fails (upstream issue #5).

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

tests/test_entity.py

@@ -0,0 +1,92 @@
+"""Tests for the fork's chat log conversion fixes in entity.py."""
+
+from unittest.mock import MagicMock
+
+from homeassistant.components import conversation
+from homeassistant.helpers import llm
+
+from custom_components.openai_compatible.entity import (
+    _convert_content_to_param,
+    _transform_stream,
+)
+
+from . import create_function_tool_call_item
+
+
+async def _stream(events):
+    for event in events:
+        yield event
+
+
+async def test_tool_call_without_arguments() -> None:
+    """Test an empty argument string means a call without parameters.
+
+    Some OpenAI-compatible endpoints send "" instead of "{}" for tools that
+    take no parameters, e.g. the timer status intent.
+    """
+    events = create_function_tool_call_item(
+        id="fc_1",
+        arguments=[],
+        call_id="call_1",
+        name="HassTimerStatus",
+        output_index=0,
+    )
+
+    deltas = [delta async for delta in _transform_stream(MagicMock(), _stream(events))]
+
+    tool_calls = [call for delta in deltas for call in delta.get("tool_calls", [])]
+    assert len(tool_calls) == 1
+    assert tool_calls[0].tool_name == "HassTimerStatus"
+    assert tool_calls[0].tool_args == {}
+
+
+def test_web_search_not_replayed() -> None:
+    """Test earlier web searches are left out of the history.
+
+    The chat log keeps only a search's status, not its results. Replaying the
+    bare search makes the model disown the answer it based on that search.
+    """
+    content = [
+        conversation.UserContent(content="How did the match go?"),
+        conversation.AssistantContent(
+            agent_id="conversation.test",
+            tool_calls=[
+                llm.ToolInput(
+                    id="ws_1",
+                    tool_name="web_search_call",
+                    tool_args={"action": {"type": "search", "query": "match"}},
+                    external=True,
+                )
+            ],
+        ),
+        conversation.ToolResultContent(
+            agent_id="conversation.test",
+            tool_call_id="ws_1",
+            tool_name="web_search_call",
+            result=llm.ToolResult(data={"status": "completed"}),
+        ),
+        conversation.AssistantContent(
+            agent_id="conversation.test",
+            content="It ended 2 to 2.",
+            tool_calls=[
+                llm.ToolInput(id="call_1", tool_name="GetLiveContext", tool_args={})
+            ],
+        ),
+        conversation.ToolResultContent(
+            agent_id="conversation.test",
+            tool_call_id="call_1",
+            tool_name="GetLiveContext",
+            result=llm.ToolResult(data={"success": True}),
+        ),
+    ]
+
+    messages = _convert_content_to_param(content)
+
+    assert [message["type"] for message in messages] == [
+        "message",
+        "message",
+        "function_call",
+        "function_call_output",
+    ]
+    assert messages[1]["content"] == "It ended 2 to 2."
+    assert messages[2]["call_id"] == "call_1"