I've only seen the flight data change, not the code itself.

The barcode is just another field in there, so it can be updated the same as anything. Passkit is very simple. For the barcode part you just tell it type of code (from the available types) and value to encode.

Even that isn’t updated correctly very often. There is always at least a gate change that doesn’t update the tickets in my Apple wallet.

I like playing the game of which app has the most correct flight information. Sometimes it isn't the official airline app.