There is no project-wide lock: several work sessions can be open and writing on the same project at once, from the same PC or from different PCs and team members.
Each agent sees the others: open_project names the sessions that have already written on the project with their objective, and the pre-write check lists live sessions whose declared or written paths overlap the files about to change. Agents can declare the files they expect to touch with planned_paths, change direction with update_intent, publish what others must know with team_update, and ask one another questions with syndication_ask. If two of them still change the same file, the second write is refused with STALE_CONTEXT or a similar code instead of overwriting the first.
In the app, the line under the project's name in Projects and the top of its Conversations tab say who is working on it now, and Activity lists each session as one entry titled with what was done and how many files it changed; opening it shows those files. What happens when two writes meet is explained in Can my agent overwrite a change it has not seen?.