test: add Phase 2 streaming SSE passthrough tests

Confirms the existing proxy streams SSE chunks incrementally:
- 5-chunk test with 50ms delays verifies time spread between first
  and last chunk arrival (not buffered)
- Verifies data: [DONE] terminator is forwarded

No src/ changes needed — Body::from_stream(bytes_stream()) already
handles SSE correctly.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

crates/cortex-gateway/tests/streaming.rs

@@ -0,0 +1,117 @@
+mod common;
+
+use futures::StreamExt;
+use serde_json::json;
+use std::time::{Duration, Instant};
+
+#[tokio::test]
+async fn test_streaming_sse_passthrough() {
+    let chunk_count = 5;
+    let chunk_delay = Duration::from_millis(50);
+    let mock_url = common::spawn_streaming_mock_backend(chunk_count, chunk_delay).await;
+    let gw_url = common::spawn_gateway(&mock_url).await;
+
+    let client = reqwest::Client::new();
+    let resp = client
+        .post(format!("{gw_url}/v1/chat/completions"))
+        .header("content-type", "application/json")
+        .json(&json!({
+            "model": "test-model",
+            "messages": [{"role": "user", "content": "Hi"}],
+            "stream": true
+        }))
+        .send()
+        .await
+        .expect("request should succeed");
+
+    assert_eq!(resp.status(), 200);
+    assert_eq!(
+        resp.headers()
+            .get("content-type")
+            .and_then(|v| v.to_str().ok())
+            .unwrap_or(""),
+        "text/event-stream"
+    );
+
+    // Collect SSE chunks as they arrive, recording arrival times.
+    let start = Instant::now();
+    let mut chunk_times = Vec::new();
+    let mut chunks = Vec::new();
+    let mut stream = resp.bytes_stream();
+
+    while let Some(result) = stream.next().await {
+        let bytes = result.expect("chunk should be valid");
+        let text = String::from_utf8_lossy(&bytes);
+        for line in text.split("data: ").filter(|s| !s.is_empty()) {
+            let trimmed = line.trim();
+            if !trimmed.is_empty() {
+                chunk_times.push(start.elapsed());
+                chunks.push(trimmed.to_string());
+            }
+        }
+    }
+
+    // Verify we got all content chunks plus [DONE].
+    assert!(
+        chunks.len() >= chunk_count + 1,
+        "expected at least {} chunks (got {}): {:?}",
+        chunk_count + 1,
+        chunks.len(),
+        chunks,
+    );
+
+    // The last chunk should be [DONE].
+    assert_eq!(chunks.last().unwrap(), "[DONE]");
+
+    // Verify the content chunks contain expected tokens.
+    for i in 0..chunk_count {
+        let chunk_json: serde_json::Value =
+            serde_json::from_str(&chunks[i]).expect("chunk should be valid JSON");
+        assert_eq!(
+            chunk_json["choices"][0]["delta"]["content"],
+            format!("token{i}")
+        );
+    }
+
+    // Verify streaming behavior: total time should reflect incremental delivery,
+    // not a single batch. With 5 chunks at 50ms each + [DONE], we expect ~300ms total.
+    // If buffered, all chunks would arrive at once after ~300ms with no spread.
+    // We verify that the last chunk arrived noticeably after the first.
+    let first = chunk_times.first().unwrap();
+    let last = chunk_times.last().unwrap();
+    let spread = *last - *first;
+    assert!(
+        spread >= Duration::from_millis(100),
+        "chunks should arrive incrementally (spread: {spread:?})",
+    );
+}
+
+#[tokio::test]
+async fn test_streaming_done_terminator() {
+    let mock_url = common::spawn_streaming_mock_backend(2, Duration::from_millis(10)).await;
+    let gw_url = common::spawn_gateway(&mock_url).await;
+
+    let client = reqwest::Client::new();
+    let resp = client
+        .post(format!("{gw_url}/v1/chat/completions"))
+        .header("content-type", "application/json")
+        .json(&json!({
+            "model": "test-model",
+            "messages": [{"role": "user", "content": "Hi"}],
+            "stream": true
+        }))
+        .send()
+        .await
+        .expect("request should succeed");
+
+    let body = resp.text().await.unwrap();
+    assert!(
+        body.contains("data: [DONE]"),
+        "response must contain [DONE] terminator"
+    );
+    assert!(body.contains("token0"), "response must contain first token");
+    assert!(
+        body.contains("token1"),
+        "response must contain second token"
+    );
+}