Use Post ID in functions.php

Only posting an alternative answer despite the question being about a 3rd-party plugin, whose source code isn’t even freely available, because I don’t believe the accepted answer is likely to be a good solution.

It’s not documented on their website, but a comment from the developer states:

These would all be considered custom requests, which our free support
doesn’t handle. What’d you want to do is probably hook into the
“booked_new_appointment_created” action which comes with the
Appointment ID (which you can use to pull down meta fields, etc.) —
That’s all the direction I can really offer you regarding these custom
coding questions.

Which implies that callback functions for the booked_new_appointment_created hook receive the appointment ID as an argument:

function add_to_system( $appointment_id ) {
    mail( '[email protected]', 'My subject', $appointment_id );
}
add_action( 'booked_new_appointment_created', 'add_to_system', 99, 1 );

Doing it this way is far more reliable, as you can be certain that the ID of the appointment you’re using is the ID of the appointment that triggered the action, and not some other post or page that might be the ‘current’ post in the global state.

This is a good rule of thumb for all hooks: Use the arguments passed to callbacks wherever possible instead of global variables.