as far as I understand:
popup notifications for new messages are only shown in the mobile app when using the push notifications service.
So there is no build in feature in the app that the app itself shows a popup and your mobile device with push notifications disabled on the rocket chat server
(e.g. like that popup the mobile browser is showing on arrival of new messages , when you are using rocket chat with a browser on your mobile device)
So the mobile app gives you only a notification when PUSH notifications are enabled on the rocket chat server, is this correct.
No. There is an in-app notification. For example, if someone write you a message, while you in other chat, that notification appears.
And if application in background push notifications come into play.
I am using the Rocket.Chat app 4.12.1 from F-Droid store on a google-free device (grapheneos).
So far it works great except for a notification on this mobile device in screen lock state when a new message arrives, the server is connected to https://gateway.rocket.chat and probably one must have play services available to get a notification.
But if this is a mandatory how for example does the mail program K9-mail operate ? This app gives an audible notification as well as a popup message instantly when new email arrives - no inscription to a special push or play service needed at all.
That would be a great improvement and feature to change from what ever app to rocket.chat.