To pull this off, the Raspberry Pi is programmed to act as a router. Any lookups that are associated with Google’s push service are redirected to a nonexistent IP and blocked from reaching your phone. When the mailbox door is opened and you place a phone inside, an ESP-32 is activated which sends a notification to the Pi that it’s okay to allow push notifications through.

I'm not well versed in networking, but this reads to me as it blocks and sends all notifications to the void and then while in the box the Pi allows new ones through.

The question then is do push notifications need an ACK and if they fail to receive one do they try again? I know cell carriers can tell when you're out of connection and can delay notifications and packets until you reconnect but this is slightly different.