bench: add CLI startup benchmark for codeflash compare --script

Measures median wall-clock time for --version, --help, auth status,
and compare --help across 30 runs with 3 warmups.

Usage:
  codeflash compare main codeflash/optimize \
    --script "python benchmarks/bench_cli_startup.py" \
    --script-output benchmarks/results.json

benchmarks/bench_cli_startup.py

@@ -0,0 +1,72 @@
+"""Benchmark CLI startup latency for codeflash compare --script mode.
+
+Run from a worktree root. Installs deps via uv sync, then times several
+CLI entry points and writes a JSON file mapping command names to median
+wall-clock seconds.
+
+Usage:
+    codeflash compare main codeflash/optimize \
+        --script "python benchmarks/bench_cli_startup.py" \
+        --script-output benchmarks/results.json
+"""
+
+from __future__ import annotations
+
+import json
+import os
+import subprocess
+import time
+from pathlib import Path
+
+WARMUP = 3
+RUNS = 30
+OUTPUT = os.environ.get("BENCH_OUTPUT", "benchmarks/results.json")
+
+COMMANDS: dict[str, list[str]] = {
+    "version": ["uv", "run", "codeflash", "--version"],
+    "help": ["uv", "run", "codeflash", "--help"],
+    "auth_status": ["uv", "run", "codeflash", "auth", "status"],
+    "compare_help": ["uv", "run", "codeflash", "compare", "--help"],
+}
+
+
+def measure(cmd: list[str], warmup: int = WARMUP, runs: int = RUNS) -> float:
+    """Return median wall-clock seconds for *cmd* over *runs* iterations."""
+    env = {**os.environ, "CODEFLASH_API_KEY": "bench_dummy_key"}
+    for _ in range(warmup):
+        subprocess.run(cmd, capture_output=True, check=False, env=env)
+
+    times: list[float] = []
+    for _ in range(runs):
+        t0 = time.perf_counter()
+        subprocess.run(cmd, capture_output=True, check=False, env=env)
+        times.append(time.perf_counter() - t0)
+
+    times.sort()
+    mid = len(times) // 2
+    return times[mid] if len(times) % 2 else (times[mid - 1] + times[mid]) / 2
+
+
+def main() -> None:
+    # Ensure deps are installed in the worktree
+    subprocess.run(["uv", "sync"], check=True, capture_output=True)
+
+    results: dict[str, float] = {}
+    for name, cmd in COMMANDS.items():
+        print(f"  {name}: ", end="", flush=True)
+        median = measure(cmd)
+        results[name] = round(median, 4)
+        print(f"{median * 1000:.0f} ms")
+
+    # Total = sum of medians (useful for a single summary number)
+    results["__total__"] = round(sum(results.values()), 4)
+
+    output_path = Path(OUTPUT)
+    output_path.parent.mkdir(parents=True, exist_ok=True)
+    with output_path.open("w") as f:
+        json.dump(results, f, indent=2)
+    print(f"\nResults written to {OUTPUT}")
+
+
+if __name__ == "__main__":
+    main()