How to convert NavigationLink tag and selection to value?

By rearranging the way properties are fed into SwiftUI, you can make it fit for the new APIs. Something like this should work:

NavigationStack {
    List(workoutTypes) { workoutType in
        NavigationLink(workoutType.name, value: workoutType)
    }
    .navigationDestination(for: HKWorkoutActivityType.self) { workoutType in
        SessionPagingView()
    }
}

NavigationSplitView {
    List(workoutTypes, selection: $workoutManager.selectedWorkout) { workoutType in
        NavigationLink(workoutType.name, value: workoutType)
    }
} detail: {
    SessionPagingView()
}

@EnvironmentObject var workoutManager: WorkoutManager
@State var presentedWorkout: [HKWorkoutActivityType] = []
var workoutTypes: [HKWorkoutActivityType] = [.cycling, .running, .walking]

var body: some View {

        NavigationStack(path: $presentedWorkout) {

            List(workoutTypes) { workoutType in

                NavigationLink(

                    workoutType.name,

                    value: workoutType

                )

                .padding(EdgeInsets(top: 15, leading: 5, bottom: 15, trailing: 5))

                .navigationDestination(for: HKWorkoutActivityType.self) { workoutType in

                    SessionPagingView()

                }

                .onChange(of: presentedWorkout) { _ in

                    guard let workout = presentedWorkout.last else { return }

                    workoutManager.selectedWorkout = workout

                }

            }

            .listStyle(.elliptical)

            .navigationBarTitle("Workouts")

            .onAppear {

                workoutManager.requestAuthorization()

            }

        }

    }

https://developer.apple.com/documentation/swiftui/navigationstack

When click the list, the stack puts the HKWorkoutActivityType data in the presentedWorkout array. So you can use onChange(of) to catch the workout your selected, and set this value to Workoutmanager.selecteWorkout.

You can also use the simultaneousGesture feature to select your workout type and replace the deprecated tag/selection.

With your code as example, something like this will do the trick.

List(workoutTypes) { workoutType in
    NavigationLink(
        workoutType.name,
        destination: SessionPagingView()
    )
    .simultaneousGesture(TapGesture().onEnded {
        workoutManager.selectedWorkout = workoutType
    }
}