I'll provide one sample stretching commonsense conceptions of languages to hint at promising directions to explore. Let's call it bridgespeak. Imagine a 2D honeycomb-like lattice of symbols. Symbols differentiate themselves across pre-attentive features like color, orientation, spatial frequency, etc. Symbols would relate to each other due to structural biases for local interactions enforced during the language creation process (i.e. during training ML models). Besides the appearance of symbols being somewhat disconnected from established writing systems (mainly due to the constraints of writing by hand on a flat surface), symbols might pack a similar amount of composable meaning to Chinese logograms which can mix together to create sentences resembling megawords (due to no explicit word delimination).
There might be a couple of similar dialects with different symbols and lattice shapes, originating from different ML models. Children would learn some of those early on due to their particular language learning abilities, in order to become familiar with the AGI's thought process. Besides, deliberate practice at later ages combined with potential social incentives to learn an interlingua might further help promote proficiency.