You can if you have them act on different apps. Otherwise it makes sense that Alfred stops you from having the same Hotkey defined multiple times, which could lead to undesirable results without you understanding why.
To have the same Hotkey do multiple things, add multiple connections.
There is no programmatic way to get selections which works on every app. Except for sending a copy command, which is why Alfred does it that way. An Automation Task would follow the same technique because it’s reliable. Plus, the sound is useful to most. And as demonstrated, it is coming from macOS, so it’s there that you’d need to mute/remove it.