Some tires have a directional arrow on the sidewall. And for mountain bike knobby tires there is often a front and rear specific lug pattern and something in the name of the tires will indicate a front or rear. For road tires if there's no directional arrow on the sidewall it makes zero difference how you mount them. But I mount them so the coloured sidewall labels, which are often only on one side, both are on the right side so the bike looks nice in pictures.

Usually the directional arrow it so that the tires ride over the belt overlap a specific way. Yet other tires have no such issues. So likely no bicycle tire needs to obey a rotational direction. Still, if there is an arrow there you may as well obey the rotational direction.

Tread on road bike tires is a case of wishful thinking on the part of the customers and marketing to suit the expectations of the buyers. Our bikes do not go fast enough with the narrow tires we use to even get remotely close to aquaplaning. Many sport motorcycle tires have minimal or no center line tread. And I know from riding such tires on wet track days and races that they stick just fine at speeds considerably higher than anyone can pedal a bicycle on the roads.