How does the Mac app know that the trial has expired?

I think there are many ways, but if there is no hidden file, it is created by describing the date and time of the first boot.If the file exists, I think the method is to calculate the elapsed time from the first boot date and time written on the file to the current boot time.I can't say exactly what name and where the hidden file is because it depends on the app.

It depends on the application.
In the application called Dash.app, there is a similar file in the folder below.

#ls [/Users/xxxx/Library/Application Support/Dash/License]
license.dash-license