[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/responses-api-proxy/Cargo.toml

@@ -26,3 +26,6 @@ serde = { workspace = true, features = ["derive"] }
 serde_json = { workspace = true }
 tiny_http = { workspace = true }
 zeroize = { workspace = true }
+
+[dev-dependencies]
+pretty_assertions = { workspace = true }