feat(rithmomachia): add usePieceSelection hook for selection state management

Extract piece selection logic from BoardDisplay into a reusable custom hook.
Provides selectedSquare, handleSquareClick, and clearSelection.

This improves testability and reduces BoardDisplay complexity by ~100 lines.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

apps/web/src/arcade-games/rithmomachia/hooks/usePieceSelection.ts

@@ -0,0 +1,83 @@
+import { useCallback, useState } from 'react'
+import type { Color, Piece } from '../types'
+import { validateMove } from '../utils/pathValidator'
+
+/**
+ * Callbacks for piece selection events
+ */
+export interface PieceSelectionCallbacks {
+  onMove: (from: string, to: string, pieceId: string) => void
+  onCaptureAttempt: (from: string, to: string, pieceId: string) => void
+}
+
+/**
+ * Hook for managing piece selection state and logic
+ */
+export function usePieceSelection(
+  pieces: Record<string, Piece>,
+  playerColor: Color | null,
+  isMyTurn: boolean,
+  callbacks: PieceSelectionCallbacks
+) {
+  const [selectedSquare, setSelectedSquare] = useState<string | null>(null)
+
+  const handleSquareClick = useCallback(
+    (square: string, piece: Piece | undefined) => {
+      if (!isMyTurn) return
+
+      // If no piece selected, select this piece if it's yours
+      if (!selectedSquare) {
+        if (piece && piece.color === playerColor) {
+          setSelectedSquare(square)
+        }
+        return
+      }
+
+      // If clicking the same square, deselect
+      if (selectedSquare === square) {
+        setSelectedSquare(null)
+        return
+      }
+
+      // If clicking another piece of yours, select that instead
+      if (piece && piece.color === playerColor) {
+        setSelectedSquare(square)
+        return
+      }
+
+      // Otherwise, attempt to move
+      const selectedPiece = Object.values(pieces).find(
+        (p) => p.square === selectedSquare && !p.captured
+      )
+      if (selectedPiece) {
+        // Validate the move is legal before proceeding
+        const validation = validateMove(selectedPiece, selectedSquare, square, pieces)
+
+        if (!validation.valid) {
+          // Invalid move - silently ignore
+          return
+        }
+
+        // If target square has an enemy piece, open capture dialog
+        if (piece && piece.color !== playerColor) {
+          callbacks.onCaptureAttempt(selectedSquare, square, selectedPiece.id)
+        } else {
+          // Simple move (no capture)
+          callbacks.onMove(selectedSquare, square, selectedPiece.id)
+          setSelectedSquare(null)
+        }
+      }
+    },
+    [selectedSquare, isMyTurn, playerColor, pieces, callbacks]
+  )
+
+  const clearSelection = useCallback(() => {
+    setSelectedSquare(null)
+  }, [])
+
+  return {
+    selectedSquare,
+    handleSquareClick,
+    clearSelection,
+  }
+}