Graceful shutdown server persistent connections with 408

[CheSema]

Lets consider to implement this approach to close connection gracefully?
https://developer.mozilla.org/en-US/docs/Web/HTTP/Status/408

There is a race condition between client and server. Client could still try to use already closed connection. It results in ugly error "No message received" or similar and retries. That could be disturbing and looks trashy. We saw that with s3. To avoid that case server could send 408 even to the idle connection right before closing it. Mozila does that, the link from it.

That race condition could be severe problem in case of max_keep_alive_requests. For example client does not honor it and keeps sending requests. At max_keep_alive_requests+1 request client receives an error.

max_keep_alive_requests introduced in #61793 (comment)_