[codex] Add use_responses_lite 'override' logic (#26487)

## Summary

- add a defaulted `ModelInfo.use_responses_lite` catalog field
- support serializing `reasoning.context` while preserving the existing
effort and summary path
- has not been turned on for any models yet

I've added an override to parallel tools if responses_lite is on. I've
also forced persistent reasoning when using responses_lite. It would be
ideal if we could centralize all the responses_lite plumbing, but I
think this is best for now to keep the plumbing & diffs small.

## Testing

- `cargo test -p codex-protocol
model_info_defaults_availability_nux_to_none_when_omitted`
- `RUST_MIN_STACK=8388608 cargo test -p codex-core
responses_lite_sets_all_turns_context_and_disables_parallel_tool_calls`
- `RUST_MIN_STACK=8388608 cargo test -p codex-core
configured_reasoning_summary_is_sent`
- `cargo check -p codex-core --tests`
- `RUST_MIN_STACK=8388608 cargo clippy -p codex-core --tests` (passes
with pre-existing warnings in `codex-code-mode` and
`codex-core-plugins`)

codex-rs/models-manager/src/model_info.rs

@@ -99,6 +99,7 @@ pub fn model_info_from_slug(slug: &str) -> ModelInfo {
         input_modalities: default_input_modalities(),
         used_fallback_model_metadata: true, // this is the fallback model metadata
         supports_search_tool: false,
+        use_responses_lite: false,
         auto_review_model_override: None,
         tool_mode: None,
         multi_agent_version: None,