It's not a technical challenge, it's a fundamental problem.

When multiple people work on a document at the same time, you will have conflicts that will become very hard to resolve. I have never seen a good UI for resolving non-trivial changes. There is no way to make this merging easy.

The only way to avoid the merge problem is to make sure that the state is synchronised before making changes. With cloud based solutions this is trivial, since the processing happens on the server.

The local first variant of this would be that you have to somehow lock a document before you can work on it. I worked on a tool that worked like that in the early 2000s. Of course that always meant that records remained locked, and it was a bit cumbersome. You still needed to be online to work so you could lock the records you needed.

It’s barely different from having multiple fat single page web apps editing a file in the cloud. All of those have local replicas of the data and present as if everyone is editing at once.

There are multiple ways to do this, like CRDTs plus raft based leader signaling for conflict resolution. The latter signaling requires almost no bandwidth. Raft based time skew adjustment works too if your problem domain can accept a small amount of uncertainty.

Like I said a lot of these same kinds of algorithms are used cloud side. All the big cloud stuff you use is a distributed system. Where the code runs is irrelevant. The cloud is just another computer.