UpdateFrom what i tested so far. I can create Checksum file for folder (Via OpenHashTab or after copying via TeraCopy) . And later check it by just clicking it. It works fine, however. It needs file's location. If i move folder anywhere else, it wont see it. However, if i do it inside folder. It works just fine if folder is moved somewhere else. HashMyFiles as well works properly.
Teracopy great for replacing Windows's copy. It not only copies well, it can also check two files via checksum. To see if files properly copied https://www.codesector.com/teracopy
Previous thread also recommended this and making torrent of folder
look into Beyond Compare. Might be what you're looking for.