Model part face in tabletop state

Replace the path->part-list store with a per-part map keyed by part id, so each placed part carries its path, stack index, and face. Derive each path's ordered children for stacking, and flip face-down parts in PartPlacement.

packages/tabletop/src/index.ts

@@ -24,7 +24,7 @@ export {
   computeSurfacePlacements,
   placementKey,
 } from './state.js';
-export type { GameState, Placement } from './state.js';
+export type { GameState, Placement, PartState } from './state.js';
 
 // Setup seeding.
 export { SetupLoader, seedFromSetup, expandSetupValue } from './setup.js';