Wire with_remote_overrides to construct model families (#7621)

- This PR wires `with_remote_overrides` and make the
`construct_model_families` an async function
- Moves getting model family a level above to keep the function `sync`
- Updates the tests to local, offline, and `sync` helper for model
families

codex-rs/core/tests/suite/prompt_caching.rs

@@ -137,6 +137,7 @@ async fn prompt_tools_are_consistent_across_requests() -> anyhow::Result<()> {
     let base_instructions = conversation_manager
         .get_models_manager()
         .construct_model_family(&config.model, &config)
+        .await
         .base_instructions
         .clone();