Migrate core test support to the shared HTTP client (#34651)

## What changed

- Send the streaming SSE request-body drain test through `HttpClientFactory`.
- Replace the test-support crate's direct `reqwest` dependency with
  `codex-http-client`.
- Remove `core_test_support` from the temporary direct-`reqwest` exceptions.

GitOrigin-RevId: 16ea4309d0b575592c2e59991eb6dce18d9467ed

codex-rs/Cargo.lock

@@ -4770,6 +4770,7 @@ dependencies = [
  "codex-features",
  "codex-home",
  "codex-hooks",
+ "codex-http-client",
  "codex-login",
  "codex-model-provider-info",
  "codex-models-manager",
@@ -4784,7 +4785,6 @@ dependencies = [
  "opentelemetry_sdk",
  "pretty_assertions",
  "regex-lite",
- "reqwest 0.12.28",
  "serde_json",
  "shlex",
  "similar",

codex-rs/core/tests/common/Cargo.toml

@@ -50,5 +50,5 @@ shlex = { workspace = true }
 zstd = { workspace = true }
 
 [dev-dependencies]
+codex-http-client = { workspace = true }
 pretty_assertions = { workspace = true }
-reqwest = { workspace = true }

codex-rs/core/tests/common/streaming_sse.rs

@@ -284,8 +284,10 @@ fn unix_ms_now() -> i64 {
 #[cfg(test)]
 mod tests {
     use super::*;
+    use codex_http_client::ClientRouteClass;
+    use codex_http_client::HttpClientFactory;
+    use codex_http_client::OutboundProxyPolicy;
     use pretty_assertions::assert_eq;
-    use reqwest::StatusCode;
     use tokio::net::TcpStream;
     use tokio::time::Duration;
     use tokio::time::timeout;
@@ -607,13 +609,16 @@ data: {"type":"response.completed","response":{"id":"resp-1"}}
             "stream": true
         });
 
-        let resp = reqwest::Client::new()
+        let client = HttpClientFactory::new(OutboundProxyPolicy::ReqwestDefault)
+            .build_client(&url, ClientRouteClass::Other)
+            .expect("build HTTP client");
+        let resp = client
             .post(url)
             .json(&payload)
             .send()
             .await
             .expect("send request");
-        assert_eq!(resp.status(), StatusCode::OK);
+        assert_eq!(resp.status().as_u16(), 200);
 
         let bytes = resp.bytes().await.expect("read response body");
         assert_eq!(bytes, response_body.as_bytes());

codex-rs/deny.toml

@@ -250,7 +250,6 @@ deny = [
         "codex-responses-api-proxy",
         "codex-rmcp-client",
         "codex-tui",
-        "core_test_support",
         # Third-party crates that own their reqwest integration. These are not part of the
         # first-party migration count above.
         "oauth2",