Your account shows a record of every appointment: studio, service, date and price. That is useful for your own reference, and you can export it along with the rest of your data at any time.
It is not a receipt, and it is not an invoice. A receipt is issued by whoever took the money, and that is the studio. Ask them for one through the message thread on that booking, and say whether you need it to carry a business name and address — anyone claiming the appointment as a business expense usually does.
Studios expect this request and most can produce one in a minute or two. If you know in advance that you will need paperwork, saying so when you book saves a follow-up later.