The lack of Apple documentation on ExtensionFoundation (and ExtensionKit) is almost funny. What can it do? What can it not do? The sum of all knowledge is: “try it and find out”.
I’ve made it as far as: myProcess = try await AppExtensionProcess(configuration: myConfig), which doesn’t cause an error and returns… but not a single line in the extension code is executed.
It’s running! Not working as intended, of course, but at least running.
Thousands of thanks to @khaost who has the only working example of iOS extensions (that I could find): https://github.com/KhaosT/UIExtensionExample
GitHub - KhaosT/UIExtensionExample: ExtensionKit demo for iOS 26

ExtensionKit demo for iOS 26. Contribute to KhaosT/UIExtensionExample development by creating an account on GitHub.

GitHub
On the other hand, I cannot upload to the AppStore because Xcode generates an Info.plist file that the AppStore rejects. Fun times.
Being desperate, I asked the question on the developer forums... and got an answer! "Ah, we didn't envision people using extensions within their own iOS apps. That's not forbidden, but it breaks the AppStore checking process. Please file bug report; we'll get back to you".
Literally, the answer was: “you're trying to create extensions that are specifically for "your" apps’ usage, and that's a distinct use case that we need to more actively consider.” (I appreciate the diplomacy in the wording)
(He confirmed that 3rd party App Extensions are still prohibited on the AppStore)
I’ve been asked to clarify potential uses, in order to help prioritize the iOS developers work (I did). @emma, @alexstaravoitau, @kebo, @lextar, I’ve seen you liking the conversation, do you want to add other use cases, or support the feedback? It’s FB20710338.
I stayed within the lines, and did not explain all the awesome things I could do with non-memory limited, third-party app extensions on iOS (separate extension for TeX! Python distributions shared between apps! Installable Unix commands!)
@nholzschuch Off the top of my head it’s probably the use cases similar to yours: firing up a Python interpreter in a separate process and in a more isolated environment. Shame it seemingly won’t work for kernels and Jupyter server though, but maybe scripts, installing packages (letting Python spawn processes via its os module perhaps?). And yes, offloading all Python interpretation to another (runtime/env managing) app is the ultimate dream haha! 😅
@alexstaravoitau @nholzschuch This! I don’t have too much to add. Running interpreters would be much safer for the main process so it is not affected by memory issues. Also updating my app without managing the distribution of all the packages would be better for everyone and we could choose both the interface and the runtime.