I know firsthand that there were a lot of people sitting on the fence who outright said they would vote for Trump if he picked Haley as a VP, but after he picked JD Vance, they were immediately repelled because they did not like the direction that signaled for term 2.
Not only that, but Haley puts in play states that were becoming competitive, but not yet listed as such, like Virginia.
So while any discussion like this is speculative, I believe that, if Trump had picked Nikki Haley as his VP, he would be pulling further ahead in Arizona, Georgia, and Pennsylvania, and he would possibly be competitive in Virginia, New Hampshire and Maine.
This is big because, if he wins Georgia, North Carolina, Arizona, and Virginia, then he has 275 electoral votes and is guaranteed victory whether he wins the belt or not.
And considering that he is performing about as well in the rustbelt, as he would be regardless of his VP choice, I think it just would have been tactically more beneficial to have chosen someone like Nikki Haley because she put into states that Trump can’t win without her.