Earth is to elevator – Elevator is to earth. Both derive Equivalence Principle which states gravity bends light but the problem is, how would one measure the initial angle when a beam of light itself is not even horizontal across the elevator resting on the ground when it has zero motion. Non-equivalency starts from here. Anyway, I believe no has tried yet to measure its value.

No, that would still be equivalency.

That is because when it is on the ground with zero motion it is exposed to gravity which causes the bending of light, just like if it was accelerating upwards.

You would measure the initial angle just like you would measure any angle for light. But the simplest way would be to control the initial angle either by having a unidirectional light source which has all bar one path obstructed, and thus the initial angle is based upon that direction, or you have a laser which is pointed in a particular direction.

No one has measured it for Earth as it is tiny.

As an approximation, for light travelling horizontally at c across a distance of w, in a gravitational field of g (or equivalently in an elevator accelerating at a=-g):

Light will take t=w/c to traverse the distance.

In this distance it will have accelerated downwards and have dropped a total of 0.5*g*t^2=0.5*g*w^2/c^2.

Ignoring the relativistic corrections, the vertical component of its velocity will be g*w/c. This means it will be travelling at an angle of atan((g*w/c)/c)=atan(g*w/c^2).

To put in some actual numbers.

Lets assume you have a horizontal light path 100 km long.

For simplicity, we will ignore the curvature of Earth.

Then due to Earth's gravity, light will have bent such that it leaves ~546 nm below where it entered and instead of travelling perfectly horizontally, it will be travelling with an angle of depression of roughly 6*10^-10 degrees or roughly 2 microarcseconds.

These are far too small to be measurable.

However gravitational lensing (i.e. gravity bending light) has been observed for other, more massive objects, like the sun.

Gain in the bending of the light beam shows an accretion in the gravitational field. So if we ignore the adjustment of an initial angle then does this mean that the said person on the floor of the elevator feels more gravity when he sees an increase in the bending of a light beam?

That depends upon what you mean by an increase in the bending. If you are ignoring the initial angle then that increase in "bending" could just be due to the change in initial angle.

However, if the initial angle is the same, then an increase in the amount of bending would require more acceleration for the elevator in deep space, or an increase in gravity for the observer on Earth.

An increase in bending (i.e. how much the slope changes) means g and a are higher.

An increase in the magnitude of the slope could be due to that, or a steeper angle.