As Smac770 mentions, that appears to be the lower support bar that sits under the radiator and holds it in place. That begs the question, what other damage has been incurred here? Is the radiator leaking? Are the electric fans still working or have they been pushed out of position or broken? If the front subframe has been bent, you're looking at a very expensive accident. Once the subframe is bent, the car will fail attempts at front-end alignment. The subframe part itself is currently $1954 at ECS tuning for a 2011 S4. I purchased one on a closeout sale for $750 from ECS back in 2016 when my car was involved in a front end accident and sustained a bent subframe (wasn't my fault and was covered by other driver's insurance). As I recall, the labor to install it was in the neighborhood of $900 at the dealer.
Hopefully you're lucky and the support bar pictured was the only structural component that was bent, and the attachment pin sheared off without bending the subframe. Those radiator support bars are generally in the $40-50 range. As ECS tuning states on their website regarding the lower support bars: "This is the support bar that sits under the radiator and holds it in place, without it your radiator has no support from below."
Out of curiosity, is the car drivable, driving normally, and not making weird noises, or was it towed? The plastic underbody cladding replacements should be relatively inexpensive -- people tear those off in driving in deep snow (frequently when backing up) or when hitting road debris (tire retreads, animal carcasses, etc). If after replacing those panels and the bent lower radiator support bar, it would be advisable to have the car aligned.
Keep us posted on where you go from here. Good luck!
EDIT: Added a picture from ECS Tuning the shows the right and left support bars (they each appear to have a couple of white zip ties on them in this picture). You can see where the bars are connected to the front radiator support. At the rear, the pins on the bars appear to go through ears on the front subframe, just above the swaybar mounts.
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