Deliberately, so you know from the start.
A tattoo is not a haircut: how long it takes depends on the idea, the area and the artist. A public calendar of free slots would leave the studio at the mercy of whoever signs up first.
Instead, you have the booking request (the client describes the idea and sends photos) and the link for a time set by you.
The accounting in the app sets the money and the paperwork side by side and gives you a file for your accountant. Invoicing and tax obligations stay with your invoicing software and your accountant.
Reminders, confirmations, deposits, aftercare and reviews: all on WhatsApp, by hand or automatically (with the WhatsApp Business API).
The only e-mail the app sends goes to the studio owner, when photo storage fills up.
The confirmation page has buttons for Google Calendar and for Apple / Outlook. The studio's calendar stays in the app.
The app never deletes consent forms or client data automatically and doesn't limit you in any way. What the law of your country says about keeping consent forms and client data is the studio's decision, not the app's.