I don't know how the Giants feel about missing out on Correa, but I think the Mets have some regret. Money's not a concern for Cohen so even if they did give Correa a 13-year deal and he crapped out on the back end, it wouldn't have a huge impact on Cohen or the Mets' finances.
The negotiations with the Mets turned into a pissing match between Cohen and Boras. That's when Correa turned back and reached out to Buxton to open the lines of communication with the Twins. The Mets' revised offer was still more than what the Twins were offering but the interest from Correa was always lukewarm at best and when the Mets and Twins had at least somewhat comparable deals on the table, C4 went where he wanted to be.