refactor: deduplicate persistence, add upsert queries, throttle snake saves

- Replace Create+Get+Update with UpsertGame/UpsertSnakeGame queries
- Extract free functions (saveGame, loadGame, etc.) from duplicated
  receiver methods on Store and Instance types
- Remove duplicate generateID from snake package, reuse game.GenerateID
- Throttle snake game DB writes to every 2s instead of every tick
- Fix double-lock in c4game chat handler
- Update all code for sqlc pointer types (*string instead of sql.NullString)

db/repository/models.go

@@ -5,50 +5,56 @@
 package repository
 
 import (
-	"database/sql"
+	"time"
 )
 
 type ChatMessage struct {
-	ID        int64
-	GameID    string
-	Nickname  string
-	Color     int64
-	Message   string
-	CreatedAt int64
+	ID        int64  `db:"id" json:"id"`
+	GameID    string `db:"game_id" json:"game_id"`
+	Nickname  string `db:"nickname" json:"nickname"`
+	Color     int64  `db:"color" json:"color"`
+	Message   string `db:"message" json:"message"`
+	CreatedAt int64  `db:"created_at" json:"created_at"`
 }
 
 type Game struct {
-	ID            string
-	Board         string
-	CurrentTurn   int64
-	Status        int64
-	WinnerUserID  sql.NullString
-	WinningCells  sql.NullString
-	CreatedAt     sql.NullTime
-	UpdatedAt     sql.NullTime
-	RematchGameID sql.NullString
-	GameType      string
-	GridWidth     sql.NullInt64
-	GridHeight    sql.NullInt64
-	MaxPlayers    int64
-	GameMode      int64
-	Score         int64
-	SnakeSpeed    int64
+	ID            string     `db:"id" json:"id"`
+	Board         string     `db:"board" json:"board"`
+	CurrentTurn   int64      `db:"current_turn" json:"current_turn"`
+	Status        int64      `db:"status" json:"status"`
+	WinnerUserID  *string    `db:"winner_user_id" json:"winner_user_id"`
+	WinningCells  *string    `db:"winning_cells" json:"winning_cells"`
+	CreatedAt     *time.Time `db:"created_at" json:"created_at"`
+	UpdatedAt     *time.Time `db:"updated_at" json:"updated_at"`
+	RematchGameID *string    `db:"rematch_game_id" json:"rematch_game_id"`
+	GameType      string     `db:"game_type" json:"game_type"`
+	GridWidth     *int64     `db:"grid_width" json:"grid_width"`
+	GridHeight    *int64     `db:"grid_height" json:"grid_height"`
+	MaxPlayers    int64      `db:"max_players" json:"max_players"`
+	GameMode      int64      `db:"game_mode" json:"game_mode"`
+	Score         int64      `db:"score" json:"score"`
+	SnakeSpeed    int64      `db:"snake_speed" json:"snake_speed"`
 }
 
 type GamePlayer struct {
-	GameID        string
-	UserID        sql.NullString
-	GuestPlayerID sql.NullString
-	Nickname      string
-	Color         int64
-	Slot          int64
-	CreatedAt     sql.NullTime
+	GameID        string     `db:"game_id" json:"game_id"`
+	UserID        *string    `db:"user_id" json:"user_id"`
+	GuestPlayerID *string    `db:"guest_player_id" json:"guest_player_id"`
+	Nickname      string     `db:"nickname" json:"nickname"`
+	Color         int64      `db:"color" json:"color"`
+	Slot          int64      `db:"slot" json:"slot"`
+	CreatedAt     *time.Time `db:"created_at" json:"created_at"`
+}
+
+type Session struct {
+	Token  string  `db:"token" json:"token"`
+	Data   []byte  `db:"data" json:"data"`
+	Expiry float64 `db:"expiry" json:"expiry"`
 }
 
 type User struct {
-	ID           string
-	Username     string
-	PasswordHash string
-	CreatedAt    sql.NullTime
+	ID           string     `db:"id" json:"id"`
+	Username     string     `db:"username" json:"username"`
+	PasswordHash string     `db:"password_hash" json:"password_hash"`
+	CreatedAt    *time.Time `db:"created_at" json:"created_at"`
 }