It's kinda sad that the only way to achieve code push in Flutter is through a third party service. I'm glad that there is still a way but still. I guess one could implement it themselfs but I cannot imagine the amount of technical difficulties there is to achieve this.
It was quite hard, I can attest. :) (Flutter Founder, Shorebird Founder here)
TIL React Native, a JavaScript Framework, now has its own Frameworks.