Let’s start with saying that the so called AI is not “intelligence”. It’s just a pretty advanced algorithm doing some “magic”. Behind the scenes it’s just a regular linear algebra equations dealing with bazillions of rows and columns feeded from the huge matrix. Modern mobile devices are capable of running “AI” models locally but it would cost a lot of power which would make a phone as unusable as Apple watch (aka charge it few times a day). So, the easy tasks like face id are done locally, more complex one (voice assistants) are outsourced to the cloud.

Is it all happening on my phone or in the cloud?

disable internet access and see what works and what doesn’t

Things that use the camera are happening on your phone.

Voice assistants are using remote services unless you’re positive you’ve setup a local privacy respecting one.

Can be either, neither is technically impossible. As another comment said, you can try for yourself what still works when your phone isn’t connected to the Internet.

You’re describing very different use cases. Face unlock isn’t AI. It’s just using biometrics to generate a very complex password. It should and can run locally, I wouldn’t trust any provider to actually keep it local though. Everything else you mentioned happens in the cloud. You need a good amount of processing power to generate the necessary output, which happens on server farms. Thats why Bezos is looking into nuclear reactors to feed his farms enough energy.