Any SwiftUI Button equivalent to UIKit's "touch down", i.e. activate button when your finger touches?

You can use a DragGesture with a minimumDistance of zero and define a closure for DOWN (onChanged()) or UP (onEnded()):

struct ContentView: View {
    @State private var idx = 0

    var body: some View {
        let g = DragGesture(minimumDistance: 0, coordinateSpace: .local).onChanged({
            print("DOWN: \($0)")
        }).onEnded({
            print("UP: \($0)")
        })

        return Rectangle().frame(width: 100, height: 50).gesture(g)
    }
}

You can create a custom view modifier:

extension View {
    func onTouchDownGesture(callback: @escaping () -> Void) -> some View {
        modifier(OnTouchDownGestureModifier(callback: callback))
    }
}

private struct OnTouchDownGestureModifier: ViewModifier {
    @State private var tapped = false
    let callback: () -> Void

    func body(content: Content) -> some View {
        content
            .simultaneousGesture(DragGesture(minimumDistance: 0)
                .onChanged { _ in
                    if !self.tapped {
                        self.tapped = true
                        self.callback()
                    }
                }
                .onEnded { _ in
                    self.tapped = false
                })
    }
}

struct MyView: View {
    var body: some View {
        Text("Hello World")
            .onTouchDownGesture {
                print("View did tap!")
            }
    }
}