Most walkers wear running shoes.
Racewalkers (competitive) tend to wear racing comp shoes with a good rounded heel, needs good flexiblilty and shoes that don't weigh much.
A bit of a lower heel is what you are looking for as walkers strike first with the heel and toe pointed up. As with running shoes some walkers have a neutral gait, some need stability and some need motion control.
There are some New Balance shoes that I use for long distance walking NB768 or 769. Asics 2140s and Mizuno Wave Inspire or the racing comps. There are some others, but again, most walkers (in racesm like Half Marathons) wear running shoes.
Tracy