This game definitely has a very charming feel! Unfortunately, it's nearly unplayable due to a major input bug. Anything else I'd have to say about the game is very minor by comparison, so I'll just focus on this. Interacting with anything gets you caught in a loop with that dialogue unless you advance the last message with a frame-perfect input. The reason for this is because the input check just looks for whether or not the button was down in that moment, so ending the dialogue and the opportunity to start the dialogue again happens within 1/60 of a second, a very short period of time that covers many times the average button press.
The solution for this is to keep track of the previous input state from the last frame or update, and compare the previous and current state. If the 'Z' button is up in the previous state and down in the current state, the player just pressed the button and you should handle the input. Conversely, if the 'Z' button is down in the previous state and up in the current one, that means the player just lifted their finger off the button. If both are down or both are up, these are states in the middle of a button press and you should ignore these inputs.
Great work on this! It definitely feels like a game that would be on the Game Boy.