バージョン古いせいかなと思ってやってみたけど
D:\learn\make\bat>make --version
GNU Make 4.3
Built for x86_64-pc-msys
Copyright (C) 1988-2020 Free Software Foundation, Inc.
License GPLv3+: GNU GPL version 3 or later <http://gnu.org/licenses/gpl.html>;
This is free software: you are free to change and redistribute it.
There is NO WARRANTY, to the extent permitted by law.

D:\learn\make\bat>make && echo meow
cmd -c test.bat
Microsoft Windows [Version 10.0.19041.1110]
(c) Microsoft Corporation. All rights reserved.

D:\learn\make\bat>exit
meow

D:\learn\make\bat>where make
c:\msys64\usr\bin\make.exe

D:\learn\make\bat>

どうやら症状は変わらないみたい