What country are you in? The device selection does vary.
That said, it just isn’t going to work if somebody pulls the chain on the light that you show because that will break the circuit to the light. The smart switch can’t make up for that.
If you are willing to just put tape over the pull chain so that it can’t be used, there are some alternatives that would give you a different manual button on the lamp that could be used without actually cutting current.
Then the socket that @johnconstantelo mentioned becomes one option, but there are other ones as well. But nothing that can work with the existing chain, unfortunately.