Related: Does the contact area affect friction forces? and https://physics.stackexchange.com/a/732573/209383.
Basically, the Amonton's law of friction stated that $$F=\mu \cdot N$$
However, in practical, I sometimes heard engineering say that less surface area led to leas friction. This is not the case where the pressure was held constant, but the normal force, i.e. "load" was held constant.
Under an extreme approximation, a wooden block of flat surface was hard to push, but if we make the surface smaller and smaller, eventually the normal force would interact through $1$ dimensional line instead of $2$ dimensional surface. The particle interactions would be changed, and, from the experience, I think some of us had found this convent to move the heavy object around.
When riding a bicycle, we knew that by selecting a tire with narrower width such as 23 cm instead of 28 cm reduced the energy lost to the friction even when the pressure and material of the tire was hold constant.
When does friction dependent on the contact area when the normal force was hold constant? i.e. what's the condition to violate the Amonton's law of friction?
