Trouble w/ smart wall switch controlling existing switched outlet/receptacle

I have an existing wall switch that controls an outlet such that if I plug in a lamp to the top outlet, the lamp can be turned on/off with that wall switch. So I thought it would be nice to upgrade that wall switch to a smart switch (specifically the GE Z-Wave

I’ve upgraded a few switches in my home already, so I thought I’m familiar with the installation by now and this one seemed pretty standard to the other ones. However, after installing it, the light on the lamp is immediately turned on after I re-engage the circuit breaker, even when the wall switch is in the ‘off’ position. Also, it sort of flickers a little bit (it’s a newer LED dumb bulb). When I flip the switch to ‘on’, the bulb flashes brighter for half a second and goes back to the on but flickering state. So in essence, I can’t turn it off from the new smart wall switch. I then unplugged the lamp and found that when the lamp is unplugged, the wall switch doesn’t even get power anymore so it disconnects from Wi-Fi and of course, the SmartThings hub. What am I doing wrong? Could such an existing switched outlet or receptacle be incompatible with a smart switch? Thanks.

sounds like your load and line may be switched