feat: configurable base_url threaded to all three client sites

Adds CONF_BASE_URL/DEFAULT_BASE_URL and threads base_url through every
AsyncOpenAI construction site: config_flow.validate_input,
__init__.async_setup_entry, and config_flow's web-search geolocation
helper (_get_location_data) — the easy one to miss, since it would
otherwise silently talk to api.openai.com when the user configured a
different endpoint.

Fixes upstream-ported fixtures (conftest.mock_config_entry,
test_config_flow's inline MockConfigEntry/data-schema assertions) to
supply base_url now that the config-flow schema requires it.

No translations/en.json exists in this repo (only strings.json), so
only strings.json got the new "base_url" UI strings.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01739Seac5eMAfNwFeiwV5r4

tests/test_base_url.py

@@ -0,0 +1,27 @@
+"""base_url must reach the OpenAI client, not just the config entry."""
+
+from unittest.mock import AsyncMock, patch
+
+from homeassistant.core import HomeAssistant
+from pytest_homeassistant_custom_component.common import MockConfigEntry
+
+from custom_components.openai_compatible.const import CONF_BASE_URL, DOMAIN
+
+
+async def test_client_built_with_base_url(hass: HomeAssistant) -> None:
+    """async_setup_entry must pass base_url to AsyncOpenAI."""
+    entry = MockConfigEntry(
+        domain=DOMAIN,
+        data={"api_key": "sk-test", CONF_BASE_URL: "http://192.0.2.10:4000/v1"},
+    )
+    entry.add_to_hass(hass)
+
+    with patch(
+        "custom_components.openai_compatible.openai.AsyncOpenAI"
+    ) as mock_client:
+        mock_client.return_value.platform_headers = lambda: {}
+        mock_client.return_value.with_options.return_value.models.list = AsyncMock()
+        await hass.config_entries.async_setup(entry.entry_id)
+        await hass.async_block_till_done()
+
+    assert mock_client.call_args.kwargs["base_url"] == "http://192.0.2.10:4000/v1"