
On my kicad, which I think is a standard install, if you go to 'Add a symbol (A)' and then type BC857 in the search box it comes up with 4 items, the first one is in a SOT-23 package so looks like the one you want. The BC857 is a fairly generic part though, it just ties down the basic part type and footprint. Once it's in the schematic you can go into it and edit the value to exactly match the Digikey part so that the BOM comes out correctly (not exactly best practise but creating a new library part for every physical part becomes a nightmare and is a little unnecessary for this).
Just checked and there isn't a drv103 in the kicad library but the one you've created looks OK. Did you create the footprint or did you use one of the ones in the footprint library?
Edit - Think this is what you have for the lower channel: And this is what you need: Thinking about it it might also be worth adding a 10-100nF capacitor across Rpulldown2. Not too sure what the ESD protection on the DRV input pin is like and if the board is used without the transistor a cap will help it survive transients better.