Why does the background look brighter after changing lenses at the same f/2.8 in studio?

First - When doing large format photography does the length of the bellows effect exposure?

When imaging we focus by moving the lens away from or towards the film or digital sensor. When imaging distant subjects the lens to image plane is most short, when imaging close, the lens to image plane is elongated. Any elongation of this lens to image distance causes the f-numbers to become invalid. If significant, under-exposure will be the result. For subject distances greater than 1 meter (1 yard) this phenomenon called “bellows factor” is infinitesimal. As we focus closer and closer “bellows factor” becomes significant. When we get close enough to achieve “unity” (life-size or 1:1), the f-numbers are 2 f-stops off. Thus “bellows factor” becomes significant at about 2 feet (600mm) and under exposure is likely. That is why the macro lens is popular, its design mitigates “bellows factor”. Additionally, modern cameras read exposure through the lens. Thus the exposure will be predicated on the camera’s ability to reverse the effect of “bellows factor”. We are talking the same danger, digital vs. film, large format vs. miniature camera.

I switched to 85mm lens and didn't change anything and made sure I am still at f/2.8 and shot the same thing. But on laptop screen I noticed the light on the background seemed to be increased!

The beauty of the f-number system is they take into account the focal length of the lens and the working diameter of lens (aperture). Thus the f-number system is universal, f/2.8 delivers same exposure regardless of focal length or working diameter. So why did you see the background change? Likely when you switched to the 85mm you repositioned yourself, i.e. you changed subject distance. That could account for this change especially if you were using a flash. Now different lenses will pass more or less light based on the number and coloration of the glass elements that comprise the lens. Most likely the lens switch changed the angle of view, you moved and recomposed. These interactions changed the way the background looked.