Where do we put an app after i pressed shutdown

The instructions in the video are for playing a sound when you log into your macOS user account. It does not get played when you shutdown the Mac.

As the person in the video said, you can name the Automator script whatever you want. You save/store it within your home user folder like you do any other document you create or edit.

There is no built-in mechanism for executing a script at shutdown.

Your option likely is going to need to approach this differently - namely have a background process start automatically and sit around idle, waiting for a TERM or KILL signal (indicating that the OS is shutting it down), then you can jump in with your sound before it quits.

Note that without some serious shenanigans (namely, writing your own Swift-based app), your script won't be able to tell the different between 'Shut down', 'Restart', or even 'Log out' - all of these would trigger the app to quit and it wouldn't necessarily know why.