### What
add wiring for `phase` field on `ResponseItem::Message` to lay
groundwork for differentiating model preambles and final messages.
currently optional.
follows pattern in #9698.
updated schemas with `just write-app-server-schema` so we can see type
changes.
### Tests
Updated existing tests for SSE parsing and hydrating from history
- capture the header from SSE/WS handshakes, store it per
ModelClientSession using `Oncelock`, echo it on turn-scoped requests,
and add SSE+WS integration tests for within-turn persistence +
cross-turn reset.
- keep `x-codex-turn-state` sticky within a user turn to maintain
routing continuity for retries/tool follow-ups.
Adds a new feature
`enable_request_compression` that will compress using zstd requests to
the codex-backend. Currently only enabled for codex-backend so only enabled for openai providers when using chatgpt::auth even when the feature is enabled
Added a new info log line too for evaluating the compression ratio and
overhead off compressing before requesting. You can enable with
`RUST_LOG=$RUST_LOG,codex_client::transport=info`
```
2026-01-06T00:09:48.272113Z INFO codex_client::transport: Compressed request body with zstd pre_compression_bytes=28914 post_compression_bytes=11485 compression_duration_ms=0
```
