feat: add facing orientation to parts

Replace the face/back boolean with a three-state facing (face, back,
standing) seeded from setup placements. Parts now orient about the
anchor at the resting face/edge, so back-down parts sit on the table
instead of below it and standing parts rest on their bottom edge.

packages/tabletop/src/state.ts

@@ -11,7 +11,7 @@
  */
 import { useMemo } from 'react';
 import { create } from 'zustand';
-import type { Candidate, Package, Route, Surface } from '@tts/bgm';
+import type { Candidate, Facing, Package, Route, Surface } from '@tts/bgm';
 
 /** The placement state of a single part on the board. */
 export interface PartState {
@@ -19,8 +19,8 @@ export interface PartState {
   path: string;
   /** The part's position in its path's stack. */
   index: number;
-  /** Whether the part's face is up (`true`) or down (`false`). */
-  face: boolean;
+  /** How the part is oriented on the board. */
+  facing: Facing;
 }
 
 /** Source-of-truth game state. */
@@ -47,8 +47,8 @@ export interface Placement {
   index: number;
   /** The number of pieces on the path. */
   stackSize: number;
-  /** Whether the piece's face is up. */
-  face: boolean;
+  /** How the piece is oriented on the board. */
+  facing: Facing;
 }
 
 interface TabletopState extends GameState {
@@ -169,7 +169,7 @@ export function computeSurfacePlacements(surface: Surface, parts: Record<string,
         piece,
         index: ps.index,
         stackSize,
-        face: ps.face,
+        facing: ps.facing,
       });
     }
   }