In Europe beauty freelancers are not really a thing, those who do it at home are typically immigrants who ask for lower prices and get paid under the table (meaning they don't declare it to taxes). On the other hand, beauty salon management app is a well-established market.

For inspiration you can look at something like timma which in the Nordics is basically a marketplace and an salon management tool. Clients find beauty salons on the marketplace, and professionals / salon owners advertise their services on the marketplace. The app solves the problems of finding clients, doing marketing, accounting, testimonials, payment, and so on.

I personally wouldn't include portfolio in the V1 of your app because most professionals already use instagram for this and you would be competing with an already established platform without clear benefit. Having a link to the freelancer's instagram in their profile is a no-brainer, of course.

Creating a marketplace from scratch is not easy and you will need a good strategy for that. What other players have done is typically offer the service to freelancers for free for a given time period and then start taking money when you have actual traffic and recognition on both side.