How can I dim out the background behind my glass head?

I tried making the glass less transparent, but then it covers the brain, which I want to keep bright and clear. As you can see in the image, the wall lights are very distracting. I also would like to get a bit more refraction in the glass, but then it distorts the brain where it is close to the edges of the glass head.

The goal is to get it to dim out the background while making the glass more glass-like without distorting or covering the brain. The brain is the focus of the infographic in my scene.

If you don’t mind bluring the entire background, you could try a post process volume and adjust the depth of field settings.

Unfortunately Newest, I just want to manipulate the part of the background directly behind the glass head.
I know there must be a material node solution, but still learning about those.