Benchmark new FastAPI server against Ktor server (10 runs)

bench.md

old_endpoint	new_endpoint	method	old_backend_mean	new_backend_mean	mean_change	old_backend_p50	new_backend_p50	p50_change	old_backend_p95	new_backend_p95	p95_change
/me	/me	GET	0.66839	0.53476	-19.99%	0.56474	0.553	-2.08%	0.88074	0.58733	-33.36%
/me/preferences	/me/preferences	GET	0.57466	0.56853	-1.07%	0.56219	0.56679	+0.82%	0.89032	0.58241	-34.69%
/me/preferences	/me/preferences	PUT	0.74	0.57	-22.97%	0.76	0.56	-26.32%	0.87	0.58	-33.33%
/code-index/projects	/projects	GET	0.86	0.63	-26.74%	0.93	0.64	-30.11%	0.97	0.67	-30.93%
/projects/{project_id}/favorite	/projects/{project_id}/favorite	POST	0.8198	0.5554	-32.22%	0.8551	0.5804	-32.13%	0.9008	0.6034	-32.96%
/code-index/query/{query_id}/vote	/query/{query_id}/vote	GET	0.7569	0.512	-32.32%	0.8343	0.5548	-33.48%	0.9591	0.5844	-39.03%
/code-index/query/{query_id}/vote	/query/{query_id}/vote	POST	0.7507	0.5553	-26.02%	0.8585	0.5778	-30.82%	0.8734	0.6085	-30.40%
/code-index/context	/context	POST	1.3786	1.1043	-19.92%	1.2944	1.1356	-12.27%	2.0348	1.2764	-37.27%
/health-check	/health-check	GET	0.8344	0.5666	-32.07%	0.8542	0.5588	-34.63%	0.8745	0.6	-37.08%
/login-with-google	/login/google	GET	1.5959	1.4463	-9.37%	1.6206	1.4193	-4.78%	1.7725	1.687	-48.95%
/code-index/query/{query_id}	/query/{query_id}	GET	0.7734	0.5756	-25.60%	0.8552	0.5752	-36.99%	0.8743	0.5861	-35.27%
/code-index/query/begin	/query/begin	POST	0.7121	0.4929	-30.82%	0.7081	0.5621	-32.40%	0.8794	0.5964	-38.42%
/code-index/query/followup/begin	/query/followup/begin	POST	0.7916	0.5715	-27.82%	0.8526	0.5705	-35.74%	0.9026	0.6045	-41.26%
/code-index/popular	/popular	GET	2.3072	0.5349	-76.83%	2.4664	0.5587	-32.86%	2.5636	0.5829	-38.16%