When I implemented Siri Shortcuts it was in the iOS 14 days, so no App Intents.
This my journal entry about it: Christopher's HealthKit App Challenge Journal - #37 by xpher0408
I referenced this tutorial https://www.answertopia.com/swiftui/a-swiftui-siri-shortcut-tutorial/, starting from the “Adding the Intents Extension” section.
In theory, it should still work with iOS 16.
At the time, I didn’t do Intents UI since you need to use UIKit for that. I think with App Intents you can use SwiftUI, but I could be wrong about that.
Seems @CalStark 's method would be the way to go for App Intents.