During eye surgery, do they only numb the cornea? Are there pain receptors deeper in the eye?

Obviously you can feel pain in your eyes from injury, trauma, headaches ect. But if, for example, you suffered an injury that extended deeper than the cornea, how much of it would you actually feel?

You know those numbing eye drops at the eye doctor they use before doing some measurements? If you had those in and then something pierced or cut your eye, would you feel it?

I promise I'm not crazy ._. saw a vid of an eye surgery and the narration said "numbing eye drops are used instead of a general anesthetic" and I know most eye surgeries you would be kept awake for anyway