Taken by itself, your final question is a very good one. The term work causes a lot of confusion for several reasons. But it literally means the transfer of energy, so using the phrase transfer of energy instead of work can often help clarify things.
The question was about static friction, so it becomes, "Do we transfer energy against static friction when we walk or ride a bike?" Well, when we walk or ride a bike we exert a static friction force backward against the floor or road. And, according to Newton's Third Law, the floor or road exerts a static friction force forward on us. With this in mind, remember that the motion or change in motion of an object depends only on the forces exerted on it by the environment, never the forces it exerts on the environment. So the floor or road is what pushes us forward, by exerting a static friction force on us. That force is actually part of the mechanism in transferring our chemical energy to kinetic energy. So we are not transferring energy against it and therefore not doing work against it.
By contrast, if we push a crate across a floor at constant speed, we are transferring our chemical energy to thermal energy in the crate and the floor. We do so against the sliding friction force which is pointed in the direction opposite to our push. So loosely speaking, we are transferring energy against the sliding friction force, and could be said to be doing work against it.