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_config_flow.py

@@ -1274,6 +1274,74 @@ async def test_subentry_web_search_user_location(
     }
 
 
+async def test_subentry_web_search_user_location_lookup_fails(
+    hass: HomeAssistant,
+    mock_config_entry,
+    mock_init_component,
+) -> None:
+    """Test the location lookup uses the subentry's model and may fail.
+
+    An endpoint that only serves other providers' models rejects the OpenAI
+    default; saving must still succeed with country and time zone only.
+    """
+    subentry = next(
+        sub
+        for sub in mock_config_entry.subentries.values()
+        if sub.subentry_type == "conversation"
+    )
+    subentry_flow = await mock_config_entry.start_subentry_reconfigure_flow(
+        hass, subentry.subentry_id
+    )
+    subentry_flow = await hass.config_entries.subentries.async_configure(
+        subentry_flow["flow_id"],
+        {
+            CONF_RECOMMENDED: False,
+            CONF_PROMPT: "Speak like a pirate",
+            CONF_CHAT_MODEL: "claude-sonnet-5-5",
+        },
+    )
+    subentry_flow = await hass.config_entries.subentries.async_configure(
+        subentry_flow["flow_id"],
+        {
+            CONF_TEMPERATURE: 1.0,
+            CONF_TOP_P: RECOMMENDED_TOP_P,
+            CONF_MAX_TOKENS: RECOMMENDED_MAX_TOKENS,
+            CONF_STORE_RESPONSES: False,
+        },
+    )
+    await hass.async_block_till_done()
+    assert subentry_flow["step_id"] == "model"
+
+    hass.config.country = "DE"
+    hass.config.time_zone = "Europe/Berlin"
+    hass.states.async_set("zone.home", "0", {"latitude": 50.9, "longitude": 12.1})
+    with patch(
+        "openai.resources.responses.AsyncResponses.create",
+        new_callable=AsyncMock,
+        side_effect=BadRequestError(
+            response=httpx.Response(status_code=400, request=httpx.Request("POST", "")),
+            body=None,
+            message="unknown provider for model",
+        ),
+    ) as mock_create:
+        subentry_flow = await hass.config_entries.subentries.async_configure(
+            subentry_flow["flow_id"],
+            {
+                CONF_WEB_SEARCH: True,
+                CONF_WEB_SEARCH_CONTEXT_SIZE: "medium",
+                CONF_WEB_SEARCH_USER_LOCATION: True,
+            },
+        )
+        await hass.async_block_till_done()
+    assert mock_create.call_args.kwargs["model"] == "claude-sonnet-5-5"
+    assert subentry_flow["type"] is FlowResultType.ABORT
+    assert subentry_flow["reason"] == "reconfigure_successful"
+    assert CONF_WEB_SEARCH_CITY not in subentry.data
+    assert CONF_WEB_SEARCH_REGION not in subentry.data
+    assert subentry.data[CONF_WEB_SEARCH_COUNTRY] == "DE"
+    assert subentry.data[CONF_WEB_SEARCH_TIMEZONE] == "Europe/Berlin"
+
+
 async def test_creating_ai_task_subentry(
     hass: HomeAssistant,
     mock_config_entry: MockConfigEntry,