Update MTPROXY_CHECK_TIMEOUT to 45s in docker-compose and documentation; adjust default timeout handling in code for improved performance under slow network conditions.

internal/checkresult/checkresult.go

@@ -3,6 +3,7 @@ package checkresult
 import (
 	"context"
 	"errors"
+	"net"
 
 	"mtproxy_checker/internal/checker"
 )
@@ -18,5 +19,9 @@ func Classify(err error) (exitCode int, message string) {
 	if errors.Is(err, context.DeadlineExceeded) {
 		return 4, "timeout"
 	}
+	var ne net.Error
+	if errors.As(err, &ne) && ne.Timeout() {
+		return 4, "timeout"
+	}
 	return 1, err.Error()
 }