Apple is not doing anything like that. Epic is lying and people who don't understand how Apple developer tools work repeat these lies.
Appel developer tools are free. Anyone can download them and use them to develop iOS, macOS, etc. apps. You don't need any special account for that. You only need an account if you want to sign your app and/or sell it on the App Store. That's it. The other thing a dev account gives you is access to pre-release software and support. And even if Epic needs access to these things, it's employees can always get individual accounts. The only thing for which they need the official "Epic dev account" is to sell Fortnite and similar games.
Unreal Engine is not an app. It is a library. Epic does not need to sign it and it does not use App Store to distribute it. Epic licenses the library to developers who then integrate them into their games and apps. Apple does not have any influence on which libraries you use. No matter whether their developer account gets banned, it has absolutely no influence on their ability to develop and test Unreal Engine. They can still get Xcode (a free software), Apple dev tools (free software), they get access to documentation (openly accessible), they can set up built servers and deploy to local iOS machines for testing. They can also get local dev accounts if they want to deploy to multiple test machines etc.
To sum it up: whether Epic has an official dev account or not has zero impact on their ability to develop or ship the Unreal Engine. If Epic stops updating the Unreal Engine, it would be 100% their decision. Epic is holding developers hostage and uses their privileged position to spread fear in order to gain advantage. Just one example of the unethical tactics Epic is using. Other being manipulating children who are addicted to Fortnite or paying off game developers to prevent them from publishing their games on other game platforms.