Last year, the corporate-dominated web came alive, much thanks to the help of corporate-owned social media platforms - how long will it take until the open sections of the web do so?

Honestly, I'm not sure how someone could come to this conclusion. The "corporate-dominated web" has been around a real long time. Remember Digg? Facebook? Myspace? We also already see several corporations using ActivityPub protocols for federation for a few years. Companies are real good at adopting technologies that work. For better or worse.

with stuff happening in the digital world that doesn’t in the real world

What? This is the real world.

it could actually be worthwile for people to immerse further into the digital world

That seems unlikely. But it's a good set of tools to use.

Could that be the actual next iteration of the web and realize what was in the past considered the “smart” web or would it be a dystopia?

I think what you're asking here is whether the "next iteration" will be users using more services? "Metaverse" is simply Facebook adding a bunch of new services beyond just facebook. Like Google does, really. Get your email, chat, social media (once upon a time), video service, books, etc. all from one place. Baidu does this too.

would it be possible to make the LLMs somehow run independently

This question doesn't make sense, TBH. Independently of what? They already run independently. You can turn off websites arbitrarily and an LLM will keep predicting the next word for you.

and how would all of that be experienced like from the user perspective

You already experience this. Whenever you use the translation app on your phone, or your phone offers the next word you might want to type? That's you experiencing this.

could the blockchain maybe be finally put to some use here?

Block chains have nothing at all to do with LLMs, or neural networks generally really. So I'm not sure if this post was produced by a prompt given to an LLM at this point.