Yes my brace had that same hole, I believe that is where my mechanic installed a rubber mount. I will check next time I'm under the car. Whatever he did it fixed the problem entirely.I noticed while re-installing my son's transmission and the support beam under it, the beam has a big hole for something (like maybe some kind of insulator) that wasn't there in my case and maybe not yours.
The front of that support beam has rubber isolators between the beam and car body where the bolts go through to mount the beam. The very rear of that beam is bolted into the body metal to metal.
As I tightened the front beam bolts down, the transmission case was resting on the metal beam - metal-to-metal.
I loosened up the front beam bolts and installed a 4"X5" piece of rubber matting about 3/16" thick into that area and tightened up the bolts hoping this will help dampen any vibrations.
Further researching this issue, I found parts breakdown listing at the link below.
It looks like there are vibration dampers but why would one near the center of the cross beam be on the "underside" of the beam?
See lower drawing of the two on the webpage linked below for the manual transmission parts.
A partial snapshot from the website page is attached below.