Adds the full documentation set for the planned desktop pet feature under docs/features/desktop-pet: README, PRD, user stories, logic design, UI design, and technical design. The pet is scoped as a lightweight always-on entry point for quick drafting, drag-and-drop staging, and task status at a glance; it does not introduce a second Ask/Execute channel, task execution path, or independent task-state store. Design only, no implementation yet.