Yes, Apple still has the advantage over OpenAI. But OpenAI can also release some iOS and Android integration layer, that allows to connect with installed apps on the device.
If Apple doesn't get their act together with the next iOS release, it could be too late.
OpenAI can't, they're completely dependent on Apple and Google permitting such a thing. Unless you have a particular way in mind they could currently achieve this?
They can integrate into third party apps, if the publishers want to. A lot of them are going to do it.
It's already possible to connect Gmail, and many other services, this can extend even more. The connection of those services could be done by the iOS/Android apps.
I doubt this will be super successful because so many of the apps that people would want to integrate it are those made by Apple, Google, Meta and others whose goal is to be a direct competitor. I might be wrong though, we'll see.
If Apple doesn't get their act together with the next iOS release, it could be too late.