Ok, so here's the misunderstanding - neural networks absolutely, 100% store information. You can download alpaca right now, and ask it about Paris, or llamas, or who invented the concept of the neural network. It will give you factual information embedded in the weights, there's nowhere else the information could be.
People probably think you don't understand databases because this seems self apparent that neural networks contain information - if they didn't, where does the information come from?
There's no magic involved, you can prove this mathematically. We know how it works and we can visualize the information - we can point to "this number right here is how the model stores the information of where the Eiffel tower is". It's too complex for us to work with right now, but we understand what's going on
Brains store information the same way, except they're much more complex. Ultimately, the connections between neurons are where the data is stored - there's more layers to it, but it's the same idea
And emergent properties absolutely are a thing in math. No sentience or understanding required, nothing necessarily to do with life or physics at all - complexity is where emergent properties emerge from