Yes there is. IDEs just aren't designed for it. The main screen in an IDE is a single branch at a time, I want to be managing a swarm of agents on multiple branches/worktrees
You don't need IDE support for this, it's all Git under the hood. Your extension can hold virtual branches in memory in the background, feed the file contents to the LLM through that layer and back, and the only problem you need to deal with after the fact is how to resolve conflicts, but the LLM would also be a good candidate to handle that. The more I think about it, the more Git makes this a straightforward implementation compared to say SVN, since branches cost nearly nothing. All of this is not to say that it's a trivial piece of work, but it is very much doable without building a new IDE from scratch.
I don't see why you necessarily need multiple machines, just multiple checkouts, one for each agent. Depends on what shared resources are involved, eg. databases, etc.