go back to auto-enabling web_search for azure (#10820)

###### What
Remove special-casing that prevented auto-enabling `web_search` for
Azure model provider users. Addresses #10071, #10257.

###### Why
Azure fixed their responsesapi implementation; `web_search` is now
supported on models it wasn't before (like `gpt-5.1-codex-max`).

This request now works:
```
curl "$AZURE_API_ENDPOINT" -H "Content-Type: application/json" -H "Authorization: Bearer $AZURE_API_KEY" -d '{
  "model": "gpt-5.1-codex-max",
  "tools": [
    { "type": "web_search" }
  ],
  "tool_choice": "auto",
  "input": "Find the sunrise time in Paris today and cite the source."
}'
```

###### Tests
Tested with above curl, removed Azure-specific tests.

codex-rs/core/src/codex.rs

@@ -719,7 +719,6 @@ impl Session {
         per_turn_config.personality = session_configuration.personality;
         per_turn_config.web_search_mode = Some(resolve_web_search_mode_for_turn(
             per_turn_config.web_search_mode,
-            session_configuration.provider.is_azure_responses_endpoint(),
             session_configuration.sandbox_policy.get(),
         ));
         per_turn_config.features = config.features.clone();