Also, my 2c:
Using Apache 2.0 basically means you are indifferent about what others use your code for. I don't see why AI training should be an exception... there are much more nefarious uses.
If you want that, make your own proprietary license. It would be no different that what other companies are doing. But know that your license would likely stop many other users from using your product as well as not be open source anymore, by both the FSF and OS definitions.
> And what might be some unintended consequences of restricting the ability for your code to be used in that way (assuming that's legally possible - and I do appreciate that it's probably practically impossible)
It would poison other (human) users of your code with your license.
There's no such thing and there never can be. Any license that bans a specific use like that would be in violation of both the Free Software Definition and the Open Source Definition.