600 requests per second for a hello world not even hitting a database? Are the units right? Shouldn't it be in kilo-requests per second?
Azure App Service has a networking stack that I would categorise as a "hot pile of steaming garbage":
It is insanely, unbelievably, almost hilariously slow. Even internally they VPN-tunnel, they NAT, and then they then do some unnecessary L7 stuff. If you can talk to App service in under 3ms, then you're lucky.
Heaven help you if you've made the mistake of separating out an "API tier" or any such thing. Using Azure SQL Database is iffy also, but no worries, support will helpfully tell you how to improve your latency from an IaaS VM... which is not what you're using if you're using App Service.
(No DB, DB calls decreases that 10x).