Outside of two really nice seasons with the Brewers in 2016 and 2018, Jacob Barnes has not been a good reliever during his big league career. He carries a 4.81 ERA in 263 games, and at 33 years old, I'm not sure there is much left to improve upon.
In 11 games for the Cardinals this year, he has a 7.15 ERA and 1.68 WHIP, which just will not get it done for St. Louis in 2024. The Cardinals have plenty of arms internally that I'd rather see out of the bullpen than Barnes, and I'm sure they will bring in a few relievers to add to that mix as well.
Barnes's presence on the roster has been fine for the second half, as they just need guys who can eat innings at times. But there is no reason to bring back Barnes for the 2024 season.