Sentences only have semantic meaning because you have experiences that they map to. The LLM isn't training on the experiences, just the characters. At least, that seems about right to me.
As to what the experience maps to, I think the simplest answer is that our phenomenal experiences are encoded as structures in our brain, but that's not necessary to understanding the difference between words that describe experiences and experiences themselves.
In the case of the brain the encoding is such that various functions "fall out of" it, like being able to relate experiences, etc.
There's no magic proposed here, this is a physicalist functionalist view.
Nothing about this prevents a computer from being sentient. As I said, none of this even matters. The key premise is that LLMs are trained on language and not experiences. Unless you believe that a description of an experience is identical to the phenomenal experience, then we agree on the key premise. Do you think that they are identical?