Gracefully shutting down a server connection that uses http2_keepalive_* errors with keepalive timeout

Version
hyper v0.14.23
h2 v0.3.14

Platform
Linux 5.11.22

Description

When gracefully shutting down a server http connection, if http2_keepalive_* options are set, then it will sometimes error with an h2 keepalive timeout before shutting down properly.

let mut http_server = hyper::server::conn::Http::new();

http_server.http2_keep_alive_timeout(tcp_idle_timeout / 2);
http_server.http2_keep_alive_interval(tcp_idle_timeout / 2);
http_server.http2_max_concurrent_streams(32);
http_server.http2_only(true);

let mut http_server = http_server.serve_connection(ingress, http_svc).with_upgrades();

// not shown: poll the connection
// not shown: receive a signal telling us to gracefully terminate connections

Pin::new(&mut http_server).graceful_shutdown();

match http_server.await {
  Ok(_) => {},
  Err(e) => {
    // `e` can sometimes be an `h2` keepalive timeout error
  }
}

Start at the Http::new(), http2_keep_alive_timeout(), http2_keep_alive_interval(), serve_connection().with_upgrades(), and graceful_shutdown() entry points shown in the report. Reproduce the HTTP/2 shutdown with keepalive settings and verify that graceful termination completes without returning an h2 keepalive timeout error.