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>

custom_components/openai_compatible/entity.py

@@ -22,7 +22,6 @@ from openai.types.responses import (
     ResponseFunctionToolCall,
     ResponseFunctionToolCallParam,
     ResponseFunctionWebSearch,
-    ResponseFunctionWebSearchParam,
     ResponseIncompleteEvent,
     ResponseInputFileParam,
     ResponseInputImageParam,
@@ -181,20 +180,13 @@ def _convert_content_to_param(
     """Convert any native chat message for this agent to the native format."""
     messages: ResponseInputParam = []
     reasoning_summary: list[str] = []
-    web_search_calls: dict[str, ResponseFunctionWebSearchParam] = {}
 
     for content in chat_content:
         if isinstance(content, conversation.ToolResultContent):
-            if (
-                content.tool_name == "web_search_call"
-                and content.tool_call_id in web_search_calls
-            ):
-                web_search_call = web_search_calls.pop(content.tool_call_id)
-                web_search_call["status"] = content.tool_result.get(  # type: ignore[typeddict-item]
-                    "status", "completed"
-                )
-                messages.append(web_search_call)
-            else:
+            # Earlier web searches are not replayed: the chat log only keeps
+            # their status, not their results, and a search without results
+            # makes the model disown the answer it based on that search.
+            if content.tool_name != "web_search_call":
                 messages.append(
                     FunctionCallOutput(
                         type="function_call_output",
@@ -217,26 +209,16 @@ def _convert_content_to_param(
         if isinstance(content, conversation.AssistantContent):
             if content.tool_calls:
                 for tool_call in content.tool_calls:
-                    if (
-                        tool_call.external
-                        and tool_call.tool_name == "web_search_call"
-                        and "action" in tool_call.tool_args
-                    ):
-                        web_search_calls[tool_call.id] = ResponseFunctionWebSearchParam(
-                            type="web_search_call",
-                            id=tool_call.id,
-                            action=tool_call.tool_args["action"],
-                            status="completed",
-                        )
-                    else:
-                        messages.append(
-                            ResponseFunctionToolCallParam(
-                                type="function_call",
-                                name=tool_call.tool_name,
-                                arguments=json_dumps(tool_call.tool_args),
-                                call_id=tool_call.id,
-                            )
+                    if tool_call.external and tool_call.tool_name == "web_search_call":
+                        continue
+                    messages.append(
+                        ResponseFunctionToolCallParam(
+                            type="function_call",
+                            name=tool_call.tool_name,
+                            arguments=json_dumps(tool_call.tool_args),
+                            call_id=tool_call.id,
                         )
+                    )
 
             if content.thinking_content:
                 reasoning_summary.append(content.thinking_content)
@@ -418,7 +400,7 @@ async def _transform_stream(  # noqa: C901 - This is complex, but better to have
                     llm.ToolInput(
                         id=current_tool_call.call_id,
                         tool_name=current_tool_call.name,
-                        tool_args=json.loads(current_tool_call.arguments),
+                        tool_args=json.loads(current_tool_call.arguments or "{}"),
                     )
                 ]
             }