Don't think it would be impossible to make an app for both iOS 3 and 26. You wouldn't be able to make it binary-compatible due to different architectures, but you might be able to use the same source code to target both OSes. You'd have to use a very old Xcode version to target iOS 3, since deployment targets this old generally aren't really supported by recent Xcode versions, and you wouldn't be able to submit that version to the App Store. Naturally you'd have to limit yourself to some subset of UIKit APIs supported back then (that hasn't been deprecated and removed). But if done right, you should be able to open up the project with a recent Xcode, hit build and run it on iOS 26.
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By the way, it looks like someone already did this (though for iOS 6): https://chatgptlegacy.com/
The app seems to be open-source too: https://github.com/bag-xml/ChatGPT-for-Legacy-iOS
It might be an impressive feat, but seems like a pointless one. Who's still got a functioning iPhone 1 - especially one with a battery worth a damn? Never mind the lack of current cellular network support.
To be fair, even with 3G networks being decommissioned, many countries still have 2G networks up and running to support older phones. Data speeds are usually way to slow to be useable, but for text messages it might work.