My client sees duplicates for the Console appointments in their Google calendar. Why is that?

If you are also using a Google calendar that is synced 2-ways with your Coaches Console calendar, then this is what usually happens:

The duplicates are not created by the Console system, but by a Google calendar functionality. It's a known (and unresolved) situation between Google calendars, which both you and the client are using. It's unresolved because Google considers it a feature, not a bug, so they never addressed it.

The Google calendars (yours and the clients') talk to each other (it's a global Google calendar feature that you cannot turn on/off) and that's what creates one instance of the appointment.

The other instance is created by the .ics file attached to the appointment confirmations and reminders that the client receives from your Console system.

Gmail/GSuite can read the data in the .ics file and places the appointment in the client's Google calendar with Google's own over-layer of invite options (yes, no, maybe); the Console does not have this invite system (so it does not originate from the Console, but from Google).

That Google appointment instance based on the reading of the .ics file stays hollow as long as the Google calendar user (your client) does not express an option (yes, no, maybe). It can be deleted to no longer see the duplicate, especially if it generates confusion.

So, if the client would not also use a Google calendar for these appointments, like you (as coach) do, s/he would not see the duplicates for the Console-scheduled appointments.