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/config_flow.py

@@ -702,31 +702,39 @@ class OpenAISubentryFlowHandler(ConfigSubentryFlow):
                     ): str,
                 }
             )
-            response = await client.responses.create(
-                model=RECOMMENDED_CHAT_MODEL,
-                input=[
-                    {
-                        "role": "system",
-                        "content": "Where are the following coordinates located: "
-                        f"({zone_home.attributes[EntityStateAttribute.LATITUDE]},"
-                        f" {zone_home.attributes[EntityStateAttribute.LONGITUDE]})?",
-                    }
-                ],
-                text={
-                    "format": {
-                        "type": "json_schema",
-                        "name": "approximate_location",
-                        "description": "Approximate location data of the user "
-                        "for refined web search results",
-                        "schema": to_openapi(location_schema),
-                        "strict": False,
-                    }
-                },
-                store=self.options.get(
-                    CONF_STORE_RESPONSES, RECOMMENDED_STORE_RESPONSES
-                ),
-            )
-            location_data = location_schema(json.loads(response.output_text) or {})
+            # Ask the subentry's own model: the endpoint may not serve
+            # RECOMMENDED_CHAT_MODEL (an OpenAI name). A failed lookup only
+            # costs the city/region hint, so it must not block saving.
+            try:
+                response = await client.responses.create(
+                    model=self.options.get(CONF_CHAT_MODEL, RECOMMENDED_CHAT_MODEL),
+                    input=[
+                        {
+                            "role": "system",
+                            "content": "Where are the following coordinates located: "
+                            f"({zone_home.attributes[EntityStateAttribute.LATITUDE]},"
+                            f" {zone_home.attributes[EntityStateAttribute.LONGITUDE]})?",
+                        }
+                    ],
+                    text={
+                        "format": {
+                            "type": "json_schema",
+                            "name": "approximate_location",
+                            "description": "Approximate location data of the user "
+                            "for refined web search results",
+                            "schema": to_openapi(location_schema),
+                            "strict": False,
+                        }
+                    },
+                    store=self.options.get(
+                        CONF_STORE_RESPONSES, RECOMMENDED_STORE_RESPONSES
+                    ),
+                )
+                location_data = location_schema(json.loads(response.output_text) or {})
+            except (openai.OpenAIError, ValueError, vol.Invalid) as err:
+                _LOGGER.warning(
+                    "Could not look up the home location for web search: %s", err
+                )
 
         if self.hass.config.country:
             location_data[CONF_WEB_SEARCH_COUNTRY] = self.hass.config.country