A piece can appear on more than one path of the same surface (e.g. the
poker deck expands to every card while the flop also places the ace), so
the render key must include the path to stay unique.
Implement the tabletop library's game state store, setup seeding with
bare-type expansion, surface mount tree resolution, part placement, and
the stacking positioning process with a dependency-free SVG path helper.
Wire the public API and add unit plus vite integration tests.