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)

snake/loop.go

@@ -62,16 +62,14 @@ func (si *SnakeGameInstance) countdownPhase() {
 				si.game.Status = StatusInProgress
 
 				if si.queries != nil {
-					si.saveSnakeGame(si.game) //nolint:errcheck
+					saveSnakeGame(si.queries, si.game) //nolint:errcheck
 				}
 				si.gameMu.Unlock()
 				si.notify()
 				return
 			}
 
-			if si.queries != nil {
-				si.saveSnakeGame(si.game) //nolint:errcheck
-			}
+			// No DB save during countdown ticks — state is transient
 			si.gameMu.Unlock()
 			si.notify()
 		}
@@ -98,6 +96,7 @@ func (si *SnakeGameInstance) gamePhase() {
 	defer ticker.Stop()
 
 	lastInput := time.Now()
+	lastSave := time.Now()
 	var moveAccum time.Duration
 
 	for {
@@ -124,7 +123,7 @@ func (si *SnakeGameInstance) gamePhase() {
 			if time.Since(lastInput) > inactivityLimit {
 				si.game.Status = StatusFinished
 				if si.queries != nil {
-					si.saveSnakeGame(si.game) //nolint:errcheck
+					saveSnakeGame(si.queries, si.game) //nolint:errcheck
 				}
 				si.gameMu.Unlock()
 				si.notify()
@@ -175,13 +174,10 @@ func (si *SnakeGameInstance) gamePhase() {
 			alive := AliveCount(state)
 			gameOver := false
 			if si.game.Mode == ModeSinglePlayer {
-				// Single player ends when the player dies (alive == 0)
 				if alive == 0 {
 					gameOver = true
-					// No winner in single player - just final score
 				}
 			} else {
-				// Multiplayer ends when 1 or fewer alive
 				if alive <= 1 {
 					gameOver = true
 					winnerIdx := LastAlive(state)
@@ -195,8 +191,10 @@ func (si *SnakeGameInstance) gamePhase() {
 				si.game.Status = StatusFinished
 			}
 
-			if si.queries != nil {
-				si.saveSnakeGame(si.game) //nolint:errcheck
+			// Throttle DB saves: persist on game over or every 2 seconds
+			if si.queries != nil && (gameOver || time.Since(lastSave) >= 2*time.Second) {
+				saveSnakeGame(si.queries, si.game) //nolint:errcheck
+				lastSave = time.Now()
 			}
 
 			si.gameMu.Unlock()