That's a huge advantage, it's means all the obvious stuff will just work. LSPs, debuggers, version control, customisation.
As much as I like Emacs, it's an insane pain to make all these things work.
If your value prop is agents on a codebase, there's no point in trying to reinvent those. They have basically been solved.
You can store the state in the SSE connection and have the problems described, and if you don't like those, you can move thr state to something distributed/persisted.
Pubsub is just a layer on top of SSE or websockets, cause guess how it'd end up sending things to the browser