A good shower curb keeps water contained in the shower area preventing you from soaking the bathroom floor.
Shower door curb edge finish.
If you cant find a suitable corner round you could finish the edge of the tile at the front of the curb or finish the front edge corner if you choose to tile the front side of the curb which i recommend with grout.
Glass tiles tumbled stone tiles and some porcelain tiles have edges that do not require a separate edge piece.
I think you should tile the whole top and front of the curb.
Shower door bottom seal 2 pack glass shower door seal strip shower door seal frameless seal shower door stop shower leaks and create a water barrier 3 8 x 39 2 4 7 out of 5 stars 166 17 88 17.
They can be installed right up to the edge of the shower and need no transition to.
I do not recommend finishing any tile edge with caulking.
A great and well made shower curb does all that and is fully waterproof.