Currently they share browser context. Adding isolated profiles is a good idea. Do you often use multiple agents in a single project and have them both work on different pages? I personally use multiple checkouts, and the problem for me is that agents working in the same project want to spin up the same dev server. And the dev servers will conflict unless I make different instances of the same project listen in their own port ranges (perhaps via a PORT env var).

We want to solve the latter by bringing better SSH support where the WebView will proxy directly to a remote machine or Docker container, so different workspaces in the vertical tabs can talk to their corresponding dev servers. But I want to hear more about your use case.