What is the best way to implement a mobile application for a website (iOS, Android)?

Question

Mobile development

There is a site. The site has authorization and other things arising from it.

I want to write a mobile application for this site.
I already had experience writing a simple mobile application for Android. There I used some site's API and saved everything in SQLite and then worked with the "local" DB in the application.

Now I'm thinking about a different approach - this is to implement (in simple terms) something like a browser that will work with the site. That is, I prepare a template on my Web server and that's it. And for smartphones I am writing a simple client that will work with this "template". Here I see advantages in the form of a simple implementation of registration and authorization, support for an authorization session, and so on (after all, this will not be on a smartphone, but on a website).
There are also advantages over conventional browsers. For example, this is an interface in which there will be no "browser stuffing", there will be only a workspace in fact.

In general, to be honest, I am new to this business and have not yet tried to write such applications, especially for smartphones. I'm sure there are knowledgeable people here. Please advise how best to implement my idea.