Does BusyCal support Push sync for Google Calendar?
BusyCal v2022.3.1 upwards supports Push sync for Google Calendar.
You can enable this by opening Settings > Accounts, selecting your Google account and changing the sync frequency to Push.
NOTE: If you have blocked BusyCal from receiving notifications from under System Settings > Privacy > Notifications or there are other external limits in place on your account, Push may not be available as an option.