You seem to have that wrong about her caving in on trans.
I do remember her vetoing an earlier bill because it was poorly written.
https://abcnews.go.com/US/south-dakota-signs-1st-anti-transgender-sports-law/story?id=82672739
Please provide a link countering this!
The Lewandowski may be the only legitimate concern
Noem vetoed the 2021 bill, claiming it was not clearly written and would have adverse economic impacts on the state (read: cave to NCAA and CoC). She then tried to backtrack by issuing two executive orders that were immediately challenged. Yes, Noem signed the 2022 bill that also added sections allowing lawsuits by the perverts. Overall indecisive behavior and not a good look for the governor.