SwiftUI DragGesture only in one direction

I'd like SwiftUI DragGesture to start only when the gesture is in a specific direction (horizontal/vertical). Is it possible?

Yes, it is, by applying one of the two components (either horizontal or vertical) of the gesture translation to the view offset.

Here's such behaviour implemented as a ViewModifier.

struct DraggableModifier : ViewModifier {

    enum Direction {
        case vertical
        case horizontal
    }

    let direction: Direction

    @State private var draggedOffset: CGSize = .zero

    func body(content: Content) -> some View {
        content
        .offset(
            CGSize(width: direction == .vertical ? 0 : draggedOffset.width,
                   height: direction == .horizontal ? 0 : draggedOffset.height)
        )
        .gesture(
            DragGesture()
            .onChanged { value in
                self.draggedOffset = value.translation
            }
            .onEnded { value in
                self.draggedOffset = .zero
            }
        )
    }

}

Demo:

struct ContentView: View {

    var body: some View {
        VStack {
            Spacer(minLength: 100)
            HStack {
                Rectangle()
                    .foregroundColor(.green)
                    .frame(width: 100, height: 100)
                    .modifier(DraggableModifier(direction: .vertical))
                Text("Vertical")
            }
            Spacer(minLength: 100)
            Rectangle()
                .foregroundColor(.red)
                .frame(width: 100, height: 100)
                .modifier(DraggableModifier(direction: .horizontal))
            Text(verbatim: "Horizontal")
            Spacer(minLength: 100)
        }
    }
}

Result: