Should the amount paid for repairing a broken laptop button be refunded to the person who broke it, especially since an alternative repair method has become available and the device has not yet been repaired?

As long as the shop owner has admitted his mistake, he is liable for what he damaged. You are only entitled to the actual cost of the error from the amount he paid you. What the second shop owner mentioned about the necessity of changing the entire keyboard is irrelevant, as long as it is possible to install the broken keys. Therefore, inquire about the cost of this installation, return the remaining amount to the shop owner, and then you have the choice to either repair the device or sell it.