Yeah you're totally right that a heavier gauge pulls the neck towards the body and generally would make the strings sit further away from the fretboard.
Another reason perhaps is that newer strings tend to sound brighter and sharper and can make fret buzz seem louder, so perhaps you had some fret buzz before but it's more noticeable with fresher strings? This has happened to me more than once.
Did you make sure you replaced the strings with ones of the same gauge? I ask because it sounds like you may have put on a heavier gauge which has caused the neck to bow with the increased tension. It's not a massive issue but if it is the case you will need to adjust the truss rod. It's a bit of a daunting process but honestly it's not too hard, there's plenty of guides out there on how to do it. Or you could take it to a shop if you're not feeling too confident.
(Edit: after reading your comment again it's more likely you replaced with a lighter gauge if the strings are hitting the first couple of frets, same solution though just turn the truss rod the other direction)
Only used connect so far so can't comment on the others. Feels nice and smooth, looks great and has some nice features. Liftoff seems to be the go to here, might check it out.