Pic of small plant bed next to driveway

Yes! Always separate the two if you can. Make the walkway the more prominent if the two, and one way to do that is to flank the walkway with planters on either side. Make it the star. And create a small cutout where the car’s driver can sort of sneak into the walkway from the side.

Wny? You already have a straight path along the driveway. It will look strange to have a parallel path right next to, plus it always looks awful to have a path that's not as wide as the slab it comes from.

I would totally remove the current path, especially the bricks which have no business on this house, plant a couple or three ornamental grasses and call it a day.

This should also be asked on the Landscape Design forum.