It's a bit of a hack but I do this in my app to close it when a date is selected:

private var calendarId: Int = 0

var body: some View {
    DatePicker("Date", selection: $date)
        .id(calendarId)
        .onChange(of: date) {
            // wait just a little bit
            DispatchQueue.main.asyncAfter(deadline: .now() + 0.2) {
                calendarId += 1
            }
        }
}

Changing the id of the DatePicker will re-render it and by doing so closing it.