Neither of those will work from what I can see. You can't mix the inputs and outputs like that. In fact, your existing button probably should not even be touched in this setup. You are misunderstanding how to wire this.
In my opinion, this Shelly device isn't really suited for this task. It is overly complicated, and doesn't appear to have just a set of relay contacts which are what is needed here. There are easier to wire devices like this device that don't require a bunch of farting around for the same price. https://www.amazon.com/dp/B08X218VMR
That being said, do you have a digital multimeter, and do you know how to use one? If so, I can probably guide you through this.