Why think that "engaging with meaning" is not in the solution-space of predicting the next token? What concept of meaning are you using?
That said, no, I don't think GPT properly grasps meaning, and my reason for that is simple: It regularly contradicts itself. It can put together words in a meaningful-looking order, but if it actually understood what those words meant as an emergent property of its design, then you wouldn't be able to trick it into saying things that don't make sense or are contradictory. If someone actually understands a subject, they won't make obvious mistakes when they discuss it; since GPT makes obvious mistakes, it can't actually grasp meaning—only brush up against it.
This argument doesn't apply to GPT because it isn't a single coherent entity with a single source of truth. GPT is more like a collection of personas, which persona you get is determined by how you query it. One persona may say things that contradict other personas. Even within personas you may get contradictory statements because global consistency is not a feature that improves training performance, and can even hinder it. Samples from its training data are expected to be inconsistent.
It is important not to uncritically project expectations onto LLMs derived from our experiences with human agents. Their architecture and training regime is vastly different than humans and so we should expect their abilities to manifest differently than analogous abilities in humans. We can be easily mislead if we don't modify our expectations for this alien context.
And the more stimuli, and the more high resolution and detailed (say at the atomic level), the more GPT's model of reality would be accurate.
Language is just symbols that stand for a stimulus (in the best case)