[codex] add responses proxy JSON dumps (#16753)

This makes Responses API proxy request/response dumping first-class by
adding an optional `--dump-dir` flag that emits paired JSON files with
shared sequence/timestamp prefixes, captures full request and response
headers and records parsed JSON bodies.

codex-rs/Cargo.lock

@@ -2552,6 +2552,7 @@ dependencies = [
  "codex-process-hardening",
  "ctor 0.6.3",
  "libc",
+ "pretty_assertions",
  "reqwest",
  "serde",
  "serde_json",