fix: make the home location lookup work against Claude

- Send the location question as a user message. A request with only a
  system message has no user content, which endpoints in front of Anthropic
  models reject ("text content blocks must be non-empty").
- Leave unknown fields out of the web search user_location. After a failed
  lookup there is no city or region, and the empty strings made every
  request fail ("user_location.city: String should have at least 1
  character").

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

custom_components/openai_compatible/entity.py

@@ -560,12 +560,20 @@ class OpenAIBaseLLMEntity(Entity):
                 ),
             )
             if options.get(CONF_WEB_SEARCH_USER_LOCATION):
+                # Leave out unknown fields: some endpoints reject empty strings,
+                # and the location lookup may have found no city or region.
+                location = {
+                    key: value
+                    for key, option in (
+                        ("city", CONF_WEB_SEARCH_CITY),
+                        ("region", CONF_WEB_SEARCH_REGION),
+                        ("country", CONF_WEB_SEARCH_COUNTRY),
+                        ("timezone", CONF_WEB_SEARCH_TIMEZONE),
+                    )
+                    if (value := options.get(option))
+                }
                 web_search["user_location"] = UserLocation(
-                    type="approximate",
-                    city=options.get(CONF_WEB_SEARCH_CITY, ""),
-                    region=options.get(CONF_WEB_SEARCH_REGION, ""),
-                    country=options.get(CONF_WEB_SEARCH_COUNTRY, ""),
-                    timezone=options.get(CONF_WEB_SEARCH_TIMEZONE, ""),
+                    type="approximate", **location
                 )
             if not options.get(
                 CONF_WEB_SEARCH_INLINE_CITATIONS,