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/queries/games.sql

@@ -1,16 +1,18 @@
--- name: CreateGame :one
-INSERT INTO games (id, board, current_turn, status)
-VALUES (?, ?, ?, ?)
-RETURNING *;
+-- name: UpsertGame :exec
+INSERT INTO games (id, board, current_turn, status, game_type, winner_user_id, winning_cells, rematch_game_id)
+VALUES (?, ?, ?, ?, 'connect4', ?, ?, ?)
+ON CONFLICT(id) DO UPDATE SET
+    board = excluded.board,
+    current_turn = excluded.current_turn,
+    status = excluded.status,
+    winner_user_id = excluded.winner_user_id,
+    winning_cells = excluded.winning_cells,
+    rematch_game_id = excluded.rematch_game_id,
+    updated_at = CURRENT_TIMESTAMP;
 
 -- name: GetGame :one
 SELECT * FROM games WHERE id = ?;
 
--- name: UpdateGame :exec
-UPDATE games
-SET board = ?, current_turn = ?, status = ?, winner_user_id = ?, winning_cells = ?, rematch_game_id = ?, updated_at = CURRENT_TIMESTAMP
-WHERE id = ?;
-
 -- name: DeleteGame :exec
 DELETE FROM games WHERE id = ?;