As you may know that critical angle is the angle of incidence beyond which rays of light passing through a denser medium to the surface of a less dense medium are no longer refracted but totally reflected. So at critical angle, the angle of refraction is 90°. As per the fundamentals of Ray optics, if we incidence a ray in reverse ie. from air to glass at an angle of 90°, the angle of refraction should be C ( critical angle ). But where exactly is the point of incidence if the angle of incidence is 90°? (You can try this with a glass cube and a laser. When I tried, the light is seemed to glare throughout the interface but did not observe any refraction)
No continuous quantity in physics is ever exact in an experimental setting.
If you wanted to get a very precise direction of travel, you would need a very wide wavefront, owing to diffraction.
In the context of the above, the concept of an incident beam precisely at $90^\circ$ is already an ill-defined concept, before you have ever inquired about where it arrives at the interface. Instead you will have to take a limit as the angle tends to $90^\circ$, and if you also require that no part of the incident beam is at more than $90^\circ$ to the normal, then you find you are talking about a beam whose width tends to infinity as the angle tends to $90^\circ$, because simultaneously the direction has to become more and more precise. Consequently the width of the region on which the incident light meets the interface also tends to infinity.
This is just a theoretical idea rather than a practical reality that the beam will come out of the angle at 90° angle when the angle of incidence is critical angle. The realistic limiting case is probably a light ray travelling at very close to a 90 degree angle of incidence. So, it would be able hit the denser medium and undergo refraction on entering the glass. as we know if the ray would be at 90°, it will not get into the medium (to the infinity) So the ray is probably less than 90°.