refactor: rename game package to connect4, drop Game prefix from types

Rename game/ -> connect4/ to avoid c4/game stutter. Drop redundant
Game prefix from exported types (GameStore -> Store, GameInstance ->
Instance, GameStatus -> Status). Rename NATS subjects from game.{id}
to connect4.{id}. URL routes unchanged.

connect4/types.go

@@ -0,0 +1,71 @@
+package connect4
+
+import (
+	"encoding/json"
+
+	"github.com/ryanhamamura/c4/player"
+)
+
+type Player struct {
+	ID       player.ID
+	UserID   *string // UUID for authenticated users, nil for guests
+	Nickname string
+	Color    int // 1 = Red, 2 = Yellow
+}
+
+type Status int
+
+const (
+	StatusWaitingForPlayer Status = iota
+	StatusInProgress
+	StatusWon
+	StatusDraw
+)
+
+type Game struct {
+	ID            string
+	Board         [6][7]int  // 6 rows, 7 columns; 0=empty, 1=red, 2=yellow
+	Players       [2]*Player // Index 0 = creator (Red), Index 1 = joiner (Yellow)
+	CurrentTurn   int        // 1 or 2 (matches player color)
+	Status        Status
+	Winner        *Player
+	WinningCells  [][2]int // Coordinates of winning 4 cells for highlighting
+	RematchGameID *string  // ID of the rematch game, if one was created
+}
+
+func NewGame(id string) *Game {
+	return &Game{
+		ID:          id,
+		Board:       [6][7]int{},
+		CurrentTurn: 1, // Red goes first
+		Status:      StatusWaitingForPlayer,
+	}
+}
+
+func (g *Game) IsFinished() bool {
+	return g.Status == StatusWon || g.Status == StatusDraw
+}
+
+func (g *Game) BoardToJSON() string {
+	data, _ := json.Marshal(g.Board)
+	return string(data)
+}
+
+func (g *Game) BoardFromJSON(data string) error {
+	return json.Unmarshal([]byte(data), &g.Board)
+}
+
+func (g *Game) WinningCellsToJSON() string {
+	if g.WinningCells == nil {
+		return ""
+	}
+	data, _ := json.Marshal(g.WinningCells)
+	return string(data)
+}
+
+func (g *Game) WinningCellsFromJSON(data string) error {
+	if data == "" {
+		return nil
+	}
+	return json.Unmarshal([]byte(data), &g.WinningCells)
+}