How do payments work with mobile Apps?

I have a SaaS website that is coded in react that uses stripe and their SDK to process payments.
I think I could easily turn this into an App for iOS and Android using react native but the question is how do payments work?
The easiest way would be to just use Stripe as I do on the website.
As far as I understood, those stores want to earn on any transaction so they will not allow me to do this.

Do I need to integrate their payment solution in this case?
Do I then have a mixed user base where parts have Stripe through the website and parts are using the integrated payment solution?

Then there is also the question about existing users that came through the website but want to use the App.
Are they now forced to pay through the app store?

How to handle the situation?

Im pretty sure all payments in app go through app store.

Payments through apps go through Google and Apple. They take 30%, by the way.