dsh-sidebar-branch-chat: Branch Chat Tab for dsh-better-sidebar

`dsh-sidebar-branch-chat` is a plugin that runs on top of `dsh-better-sidebar`, providing users with a dedicated “Branch Chat” tab. By leveraging sandwiched context inheritance, shared tools, and permissions, it enables the creation of isolated sessions that are archived immediately, without polluting the main conversation history. The plugin supports branch switching, model selection, and instant archiving, making it suitable for context-isolated testing and exploration.