feat(tabletop): add state, setup, mounting, and stacking

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.

packages/tabletop/src/placement.tsx

@@ -0,0 +1,30 @@
+/**
+ * `PartPlacement` — position a part on a surface location.
+ *
+ * A stable per-part component that places a part at its route's anchor (plus
+ * the candidate's anchor when there is one) and applies the route's stacking
+ * strategy via `useStacking`. Renders the part's mesh with `PartView`.
+ */
+import type { Package } from '@tts/bgm';
+import { useStacking } from './stacking.js';
+import type { Placement } from './state.js';
+import { PartView } from './partView.js';
+
+export function PartPlacement({ pkg, placement }: { pkg: Package; placement: Placement }) {
+  const { route, candidate, piece, index, stackSize } = placement;
+  // `piece` is `package:type#id`; the parts map is keyed by `type#id`.
+  const part = pkg.parts.get(piece.split(':').slice(1).join(':'));
+  if (!part) return null;
+
+  const { x, y, rotation } = useStacking(route.stacking, index, stackSize);
+
+  const anchorX = (candidate?.x ?? route.x ?? 0) + x;
+  const anchorY = (candidate?.y ?? route.y ?? 0) + y;
+  const anchorRotation = (candidate?.rotation ?? route.rotation ?? 0) + rotation;
+
+  return (
+    <group position={[anchorX, 0, anchorY]} rotation={[0, anchorRotation, 0]}>
+      <PartView part={part} baseUrl={part.baseUrl} />
+    </group>
+  );
+}