If your threat model is such that it's perfectly fine for the server to know everything that's coming from and going to the client, there's no problem at all. That's probably your situation, it's okay that the server knows what notifications it's sending to your app.

If your threat model is such that you'd rather not have the server know what's sent to and from the client, it's not enough to just encrypt the data in flight, which is what HTTPS does. With encrypted chat, we typically want what we refer to as end-to-end encryption, where the server can't see the content of messages sent between users.