Extract Responses header conversion into a shared module (#48200)

Move JSON-to-HTTP header conversion from `responses_websocket` into the
crate-wide `responses_headers` module and update the WebSocket code to use it.
Preserve conversion of string, number, and boolean values, while continuing to
ignore invalid header names and unsupported or invalid values.

GitOrigin-RevId: f179de214cf763549b5b8a898dc4bcda3ce07ebd

codex-rs/codex-api/src/lib.rs

@@ -8,6 +8,7 @@ pub(crate) mod images;
 pub(crate) mod provider;
 pub(crate) mod rate_limits;
 pub(crate) mod requests;
+mod responses_headers;
 pub(crate) mod safety_buffering;
 pub(crate) mod search;
 pub(crate) mod sse;