Some additional pictures of the whole box at various angles would definitely help. Do the white and black wires attached to that switch go into the same cable, and are there any other color wires in the same cable Since it's on a different circuit, it's quite possible the power is run to another point (perhaps the pool light junction box, or another junction box outside), and that only a 2-wire (plus ground) switch leg is going to the switch. If that's the case, you won't be able to install any neutral-required switch for it there. You can't tap neutrals that might be there for the other switches on another circuit (both by code and because it would trip the GFCI anyway). The white wire there is actually hot (it's supposed to be taped/painted/marked black, but that's often not done).
If it's going to another junction box outside (not the special pool light box), you might be able to install the Kasa switch there depending on location, though you'd lose the ability to control it from the switch inside and have to use the app (there are some ways to add a "dummy" switch to trigger the light but let's not confuse things yet).
But get us some more pictures and we'll help out...
