It's the reflection and not the lighting, and because it has no HDRI it is reflecting the Environ/Backplate color, which is bright (see later about that).
Best to give it the HDRI that is being used in the environment - since it is not a spherical image, would have to use Screen projection in the bitmap, and I used Do not alter projection in the Shadowcatcher. Final image rendering dimensions will need to match the backplate to avoid squashing or stretching it. I used Always Solid mode so that we could grab the background in the image rather than composite in post for these IR tests. The reflection changes of course, as one has the solid material it is reflecting, the other has the backplate through the shadowcatcher.
Or you could use a much darker Environ/Backplate color in the shadowcatcher. Also note that the offscreen rays play a part - since this is a screen mapped image and not a spherical HDRI, when rays go off the screen then I am not sure what color they get :) I got a close match by grabbing the color from an IR of the solid material into a CoronaColor, passing it through a tonemap so it is not affected by post processing (as the color you have grabbed from the VFB for the solid material has already gone through that post processing, with an amplified Exposure, so using that same color as the background color just gets brighter as the Exposure is applied to it again, in effect exposing it twice), and using that result in the Backplate and the Off-screen color map (disabling Use enviro for offscreen rays).
As a note, there was a mapping offset of 0.5 in the U of the bitmap used as an environment, not sure what effect that might have too.