Its been a while since I made the original system, but here is a basic rundown on how the save codes work.
First of all, the game doesn’t actually remember what items and stats you have unlocked, it instead gets the data from the save code, and gives the progression stuff accordingly. It does this by getting your current status for things like XP, Trophies, ect and then putting each of the stat numbers into a end game widget. Then it has you put each number back into a counter, and has each counter connected to a stat (like XP, Trophies, ect).
In Depth Explanation
Lets say you have three trophies in a “Trophy#” property. Once the game ends, the program then has another property (We can call it “Code”) which puts the current value of “Trophy#” along with any other properties you have. Then the end game widget displays that new property for your new save code.
To collect the data after starting a new game, the game has you put each number of your save code into a counter (one counter per stat), the counter adds its data to the property called “Trophy#” to add back your original number of trophies earned.