docs(loadtest): add pool_check.py to README and remove dead open_connections_to helper

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

Author: yoon-park-rl

loadtest/README.md

@@ -20,11 +20,16 @@ client + server _request handling_ from provisioning.
 | `h2_single_conn.py` | Raw `httpx` HTTP/2 on a single warmed connection (50-request burst). |
 | `raw_fetch_test.py` | Raw `httpx` HTTP/1.1 keep-alive baseline. |
 | `alpn_check.py` | Confirms the origin negotiates `h2` via TLS ALPN. |
+| `pool_check.py` | Verifies that multiple sync `Runloop` instances share a single connection pool (transport object identity check, no real requests). |
 
 The raw-transport probes compare httpx HTTP/2 multiplexing against HTTP/1.1
 directly — the same comparison that motivates the SDK's shared HTTP/2 pool.
 They're kept so the comparison stays reproducible.
 
+`pool_check.py` is a lightweight sanity check (no API key, no real requests) that
+confirms multiple sync `Runloop` instances reuse a single underlying transport
+object — preventing file-descriptor exhaustion when many clients are instantiated.
+
 ```sh
 # Install the SDK from this checkout (editable):
 cd /path/to/api-client-python && uv sync

loadtest/pool_check.py

@@ -25,18 +25,6 @@
 N = 20
 
 
-def open_connections_to(host: str) -> int:
-    """Count ESTABLISHED TCP connections to *host* via lsof."""
-    try:
-        out = subprocess.check_output(
-            ["lsof", "-i", f"@{host}", "-sTCP:ESTABLISHED", "-n", "-P"],
-            stderr=subprocess.DEVNULL,
-            text=True,
-        )
-        return max(0, len(out.strip().splitlines()) - 1)  # subtract header
-    except Exception:
-        return -1  # lsof unavailable
-
 
 def main() -> None:
     fd_before = resource.getrlimit(resource.RLIMIT_NOFILE)[0]