There’s no way within web standards to match iOS native api UX. Even on Android where you have chrome as the mobile browser you can’t match it.
Even if you could ship chrome renderer on iOS you won’t be able to make a mobile web app feel as good as an iOS app. The little details, animations, and microinteractions that come with native apps are better, plus there are other less visiual capabilities like background uploads and prefetching. The moment you need something like an in app camera, a native app is going to be so much better.