That's how one of the black wires was looped around the switch. Does that make a difference?

@M-I-Z  it looks like the black wire with the loop is your line wire. Turn the breaker off.  I'd cut the wire back and put a pigtail on it. Connect your green ground wire first. Next, connect all the white neutrals to each other. Next connect your load wires to the load terminal (The ones that go from the box to the lights). With the pigtail you created, have one wire go to one switch and another wire go to the kasa line terminal.  Turn the breaker back on.

@M-I-Z 

Don't separate out your Neutrals - leave them all connected as per they were originally and just ADD your white wire from the Kasa (so now you have 4 wires total in that wire nut) 

The Black wire connected together on the Switch terminal  in a loop originally - cut the loop, then strip about 1/2" on both ends; then connect them together and add the Line Wire from the Kasa in a wire nut i.e. 3 wires in that Wire nut 

The other Black Wire - connect that to the Load Kasa Wire with a Wire Nut (2 wires total) 

Changing Ground will make no difference - Ground wire is not an 'active' part of circuit, it is only there for personal safety 

Using your original pics, this is what you should have