Update README and Docker documentation to clarify exit codes and error handling. Introduce new error for no data received after MTProxy header in checker logic.

internal/checker/checker.go

@@ -16,6 +16,10 @@ import (
 // ErrProxyClosed indicates the MTProxy dropped the TCP connection right after the probe (Telethon #1134 style).
 var ErrProxyClosed = errors.New("mtproxy closed connection after initial payload")
 
+// ErrNoDataAfterHeader indicates the proxy accepted the probe but sent no application data back within the wait window.
+// Treating silence as success matched some servers but often disagrees with Telegram client "unavailable".
+var ErrNoDataAfterHeader = errors.New("no data from proxy after mtproxy header (timeout)")
+
 // Check runs the handshake probe for the given parsed secret.
 func Check(ctx context.Context, host string, port int, parsed *secret.Parsed, dcID int16) error {
 	conn, err := dialTCP(ctx, host, port)
@@ -101,5 +105,5 @@ func waitPostPayload(conn net.Conn) error {
 		}
 	}
 	_ = conn.SetReadDeadline(time.Time{})
-	return nil
+	return ErrNoDataAfterHeader
 }