It's true that a transverse wave, by definition, propagates perpendicular to its direction of motion. However, in the case of electromagnetic waves, they are not limited to the presence of physical surfaces. Electromagnetic waves can propagate through empty space, including free space, without requiring a physical surface.
Electromagnetic waves are a result of the interaction between electric and magnetic fields. According to Maxwell's equations, when electric charges accelerate or oscillate, they create time-varying electric and magnetic fields that can propagate through space. These oscillating fields support the formation and propagation of electromagnetic waves.
In free space, electromagnetic waves are not bound by physical surfaces but instead propagate as self-sustaining disturbances in the electromagnetic field. They consist of perpendicular oscillating electric and magnetic fields that are in phase with each other and propagate through space in a direction perpendicular to both the electric and magnetic field vectors. This behavior allows electromagnetic waves to traverse empty space and propagate over long distances.
While electromagnetic waves can interact with surfaces and undergo reflections, refractions, and other phenomena when encountering boundaries between different materials, they are not strictly limited to the presence of surfaces. In free space, electromagnetic waves can propagate as transverse waves without requiring physical surfaces for their formation and propagation.