How does one go about getting a listing like this? I am new to iOS and macOS and I'd like to learn. Can I pull the equivalent of a iOS ".apk" file and decompile it like Android?

If you download the iOS application in iTunes, or sync your applications from your device to iTunes, then you can drag the applications out of iTunes onto your desktop. That's an IPA file, which is essentially a zip file following a specific format. Just rename from .ipa to .zip and unzip it. You can now inspect the application's contents.

One method: navigate to the file in the Mac OS Finder, right-click on the icon, choose "Show Package Contents" from the contextual menu.

Yes, you get ipa file for application, which is pretty much zip file (same as apk). Unpack it and you'll get folder structure you see in screenshot.