Every discussion on the desktop app has a workspace: a folder on your machine. The room reads and writes there and nowhere else unless you say otherwise.
Choosing one
Pick a folder when you start a discussion, or let the app propose the one the project already uses. A discussion filed in a project works where that project's other discussions work — so a new question about the same codebase lands in the right checkout without being told.
A discussion with no folder is a chat-only room. It still has the full room and the full review, it just has no hands.
Its own branch
A discussion can take a worktree of its own: a separate checkout on its own branch, made from your current HEAD. Your working tree is untouched while the room works, and at the end you merge the branch, open a pull request from it, or throw it away. That is what makes it safe to run several discussions at once on the same repository.
Without one, the room works directly in your checkout. That is fine and often what you want; the app is clear about which it is, and says so on the discussion's Details.
Multitasking
Several discussions can run at once, each in its own workspace. A discussion that finishes while you are looking at another marks itself unread in the sidebar, and the tray tells you.
Where it says so
The workspace — folder, repository, branch, and whether it has its own checkout — is on the discussion's Details, on every device. The phone and the browser have no checkout of their own, so this is how a discussion read there says which repository it is about.