On iOS, the OS does not track which applications are browsers, and as for the system, the user must use Safari for everything. Therefore, the API does not look like a question related to macOS related to you.
However, if you want your application to appear in the Open pop-up window, you can set your application as capable of opening certain types of documents . There are many system-declared document types , but you can highlight network-related ones such as public.html ( kUTTypeHTML ).
Unfortunately, I'm sure iOS doesn't allow apps to declare support for opening simple http URLs, only custom URL patterns, but you can still declare support for certain file types, such as HTML, just in case the user tries open it up. Here is an example:
First, you need to tell Xcode which documents you support, you do this by choosing your purpose, sending information and adding document types:

Then, at any time when your application is prompted to open the .webarchive file, this document describes how you should open it. Basically, since you donβt own the file type, you can just look inside the parameter dictionary in application:didFinishLaunchingWithOptions: or application:willFinishLaunchingWithOptions .
func application(_ application: UIApplication, didFinishLaunchingWithOptions launchOptions: [UIApplicationLaunchOptionsKey : Any]? = nil) -> Bool { if let url = launchOptions?[UIApplicationLaunchOptionsKey.url] as? URL {
Thus, in reality, AppDelegate will most likely delegate this to another part of your application, simply by passing it the URL .
But then again, the user probably wonβt be able to just go to Safari and just share the web page with your application. Your application will most likely only show up when the user actually clicks share on the actual html file, but this is probably the closest thing that iOS offers for what you want.