net/http: check server shutting down before processing the request

The root cause of issue #65802 is a small race condition that occurs between
two events:

1. During the HTTP server shutdown, a connection in an idle state is identified
and closed.
2. The connection, although idle, has just finished reading a complete request
before being closed and hasn't yet updated its state to active.

In this scenario, despite the connection being closed, the request continues to
be processed. This not only wastes server resources but also prevents the
client request from being retried.

Fixes #65802

Change-Id: Ic22abb4497be04f6c84dff059df00f2c319d8652
GitHub-Last-Rev: 426099a
GitHub-Pull-Request: #65805
Reviewed-on: https://go-review.googlesource.com/c/go/+/565277
LUCI-TryBot-Result: Go LUCI <[email protected]>
Reviewed-by: Carlos Amedee <[email protected]>
Reviewed-by: Sean Liao <[email protected]>
Reviewed-by: Damien Neil <[email protected]>
Auto-Submit: Sean Liao <[email protected]>

Author: WineChord

src/net/http/server.go

@@ -2006,6 +2006,9 @@ func (c *conn) serve(ctx context.Context) {
 			// If we read any bytes off the wire, we're active.
 			c.setState(c.rwc, StateActive, runHooks)
 		}
+		if c.server.shuttingDown() {
+			return
+		}
 		if err != nil {
 			const errorHeaders = "\r\nContent-Type: text/plain; charset=utf-8\r\nConnection: close\r\n\r\n"