This looks like a pretty cool project. The syntax removes a lot of the complexity of tex, while still being fairly similar.

I see how this could be attractive especially to new students.

What I haven't seen (and hopefully I just missed it) is a way to run this locally. Would my documents be permanently tied to the typst online editor?

If that is the case than I don't think it has any real chance of adoption. They cease to exist and my raw documents become instantly worthless.

Not to mention offline editing, etc.

It looks potentially promising, but also very worrying with the cloud and corporate influence in style. It states that offline is available, which is good - but it appears as somewhat of an afterthought. A good contender would be something that is more of an 'offline-first' mentality, with cloud capabilities provided by a separate project, rather than rolled together as one. There are far too many companies trying to use the internet as disk space, when it should be obvious why it's a terrible idea due to the low internet speeds and high latency that most of the world still has to deal with. It would be wonderful to see things be local first, with some very deliberate effort required to opt-in to cloud features.

I'll need to have a play but the screenshots look more like a prettier latex than a fundamental phase transition.

Can you invide me to typst?

LaTex is the C++ equivalent in the world of typesetting languages. You can do amazing things with it and have a pixel perfect document at the expense of very high complexity.

If you install a LaTeX environment I just press compile and it goes, where is the fixing?