Archery is a sport that need a lot of skill and a lots of concentration. The last thing that an archer needs is pain or discomfort in their feet to distract them. They also do not want shoes that are unstable and causing too much excursion of the center of gravity when they are trying to aim the bow to shoot the arrow.
There are no specific archery shoes like there are specific shoes for other sports. It would make sense that the shoe fits well and is comfortable and has some support as the archer does have to spend many hours standing on the foot. Some support in the shoe may be helpful for that. Foot orthotics in archery many also help increase stability and reduce the excursion of the center of mass.
Some archers use running shoes, but the maximalist cushioned running shoes might be a bit on the unstable side when you want to maximize stability. Some archers prefer to use the weightlifting shoes as they are a good base to put your foot on. Shoes used in other sports may also be useful.
If you are an archer and are looking for the best shoe, then it might be a matter of trial and error until you are comfortable with the shoe that suits you the best.