Is the money that was not withdrawn from the bank account after purchasing an airplane ticket permissible or impermissible, and what should I do with it?

Since the ticket vendor has acknowledged receiving the payment, the error might be with the bank or in your account. You should contact the bank to correct the error if it originated from them. If no error is found on their part, then you are not liable for anything, and you may utilize your money. However, if it is proven that a certain entity is entitled to an amount, then you are obliged to pay it. But you are not obliged to refrain from disposing of your money merely due to doubt.