Some people apparently has already mentioned Toga (see https://toga.beeware.org), the GUI framework, however I'd like to go a bit more in-depth into how all this stuff works. Also, just to add, Briefcase (https://briefcase.beeware.org) is the packaging tool that turns a Python codebase into an Xcode project, installing all dependencies in the process.

So... how is Python running on iOS in the first place? Well, Python is written in C and uses autoconf, so it's possible to compile it for iOS with a bunch of additional handling -- with things like platform identification and more annoyingly, packaging Python properly so it could be distributed through the app store. This includes using Apple's "framework" directory structure and not installing any platform-specific tools, and making each binary extension module a separate "framework" in Apple's sense. And of course, the whole lot of C APIs that Apple has helpfully disabled. References: https://docs.python.org/3/using/ios.html and the whole thread of PRs is at https://github.com/python/cpython/issues/114099 -- this part of functionality is made possible with Python 3.13 officially, and has been maintained in https://github.com/beeware/Python-Apple-support/ and -patched branches of https://github.com/freakboy3742/cpython/ before. CPython still lacks some infrastructure for iOS builds and has not added tvOS/watchOS/visionOS yet so these two repositories serve these purposes as more things gets integrated into official CPython.

Now you would have Python running on iOS, but you'd need a way to access objc APIs. Rubicon Obj-C (https://rubicon.beeware.org/) is a shim that does exactly that, created by the BeeWare project as well. Since the Objective-C runtime is all C underneath it, and Python provides ctypes to call C functions, Rubicon Objective-C thus works by calling the appropriate C functions to send the appropriate messages using the Objective-C runtime, thus being able to access all native Objective-C APIs.

To start this Python code that does all the interesting stuff, however, the Python C API is used. The template that Briefcase uses to roll out Xcode projects with Python code is found at https://github.com/beeware/briefcase-iOS-Xcode-template and consists of a bulky part of initialization as seen in the main Objective-C file.

Toga's iOS backend uses Rubicon Objective-C to access the native Objective-C classes to make a UIApplication, UIWindow, UIViews, and all the native controls.

A really good conference talk by Dr. Russell Keith-Magee, founder of Toga, explains how this all works not only on iOS as I described above but also on Android.

I'm putting this info here just in case you're curious or if you'd like to try to embed Python and access the raw Objective-C APIs by yourself. Toga, however, is getting more mature almost every day, and besides simply wrapping the iOS APIs as described above, it is significantly more Pythonic and it abstracts away all the small cross-platform differences of apps on multiple platforms, so if you write a Toga app you can also deploy it on Windows (Winforms), Linux (GTK+), macOS (Cocoa), Android -- although some functionality may not be fully available.

DISCLOSURE

I have contributed to (but am not affiliated with) this project and therefore may be biased, however I have ensured that all my statements above are truthful in terms of the current state of the project. I am NOT AFFILIATED with the BeeWare project; just trying to spread some news of it.

EDIT and if you want to interact with the Python runtime in Swift you may utilize PythonKit: https://github.com/pvieito/PythonKit -- this is not related to BeeWare nor official CPython which were projects I have been talking about earlier.