chore: Eliminate `as any` casts in Game/index.ts with proper type definitions

[nodots]

Problem

src/Game/index.ts contains 46 as any casts on the feat/4.6.4-RC branch. These bypass TypeScript's type safety and mask potential runtime bugs. Key categories:

1. Undo stack (activePlay.undo) — ~6 casts

The undo feature stores undo.frames on activePlay, but BackgammonActivePlay doesn't define an undo field, forcing (game as any).activePlay patterns everywhere.

2. Doubling cube offeredThisTurnBy — ~3 casts

The per-turn repeat-double guard uses (game.cube as any).offeredThisTurnBy because the BackgammonCube type doesn't include this field.

3. Game/Play state assertions — ~11 casts

Generic return types from state transitions are cast to any instead of using proper discriminated union narrowing.

4. Move property modifications — ~11 casts

Mutating move properties via as any instead of using typed builder patterns.

5. Generic return type casts — ~5 casts

Functions returning as any to satisfy return type constraints.

Implementation Plan

Phase 1: Update @nodots-llc/backgammon-types (prerequisite)

1. Add undo field to BackgammonActivePlay type:

   undo?: { frames: BackgammonGame[] }

2. Add offeredThisTurnBy to BackgammonCube type:

   offeredThisTurnBy?: BackgammonPlayer

3. Add stateVersion to BackgammonGame if not already present:

   stateVersion: number

Phase 2: Eliminate casts in src/Game/index.ts

4. Undo stack casts — Replace (game as any).activePlay with properly typed access now that types include undo
5. Cube casts — Replace (game.cube as any).offeredThisTurnBy with direct access
6. State transition returns — Use TypeScript discriminated unions and type guards instead of as any casts. Example:

   // Before
   return { ...game, stateKind: 'moved' } as any
   // After  
   return { ...game, stateKind: 'moved' as const } satisfies BackgammonGameMoved

7. Move mutations — Create typed helper functions for move property updates

Phase 3: Verify

8. Run npx tsc --noEmit — should compile with zero errors and zero as any
9. Run full test suite to verify no regressions
10. Search for remaining as any and document any that are truly necessary (e.g., third-party lib interop)

Files to modify

• ../types/src/ — type definitions (Phase 1)
• src/Game/index.ts — remove casts (Phase 2)
• src/Play/index.ts — may have related casts

[nodots]

Tracked under epic #133 (Game/index.ts remediation), alongside the decomposition issue #132. See the epic for sequencing.

[nodots]

Verified the undo-cast type constraint while planning #132: the earlier "types→core circular dependency" framing is inaccurate. BackgammonGameMoving is defined in this same types package (packages/types/src/game.ts:193). Typing undo.frames as BackgammonGameMoving[] only forms a play.ts ↔ game.ts file cycle within @nodots/backgammon-types, which is harmless for a type-only import type (erased at compile time). So the undo casts can be deleted after promoting undo? from BackgammonPlayMoving to BasePlay — no any[] fallback needed.