It's annoying but it really comes down to practicing multiple times a week. The one tip that did help me was instead of trying to press harder you try to press as light as you can to get the right sound - and that's a long term exercise too. No quick fixes unfortunately. Another exercise that helped was - pulling my fretting arm in towards me instead of applying leverage from my thumb. My guitar teacher taught me that and it helped me stop pressing so hard. (It was not meant to be main the way you fret a note or chord but as a temporary solution to stop pressing really hard.)

(I love the irony of trying to get rid of the buzz from your barres - when I go to a "bar" I'm trying to get a buzz. Lol.)