Yup. Welcome to the Democratic Party
It's not just "the Democratic Party" though. Klobuchar is notably more hawkish than everyone else in the 2020 Dem. field, even (like Hillary Clinton at one point) having been in favor of a no fly zone in Syria.
Gillibrand also co-sponsored the "Free" Syria Act with her.
She's par for the course for most Dems. Not that that's a good thing.
Gillibrand, unlike Klobuchar, voiced skepticism of the US being involved in Syria at all by 2015:
https://www.cbsnews.com/news/sen-gillibrand-obamas-syria-strategy-wont-work-long-term/
Gillibrand also sounded ambivalent about the US mission in Libya back in 2011:
https://observer.com/2011/03/on-libya-gillibrand-and-nadler-sound-different/
And of course, Gillibrand, like the majority of Senate Dems, was critical of both of Trump's attacks on the Assad regime for chemical weapons use, while Klobuchar called it "the right thing to do".
Klobuchar also voted for the anti-BDS bill, while nearly all of the other 2020 Dems voted against it. None of the others running or looking to run for prez in 2020 are as hawkish as her, as far as I can tell.
Gillibrand do what is base for her career at that moment remember her stance on guns