in general, posting a floor plan would be helpful for us.

a partition won't stop cooking odors or appliance noises. fridges run pretty much all the time now (more efficient) and ovens are noisy as all get out (fan to cool electronics.)

if the point of the partition is to screen kitchen mess and define the space, go for it. for noise and odor, just skip it, its not going to help at all.

The only way you'll lessen "cooking odor leakage" is by installing (and faithfully using!) a properly sized and installed exhaust fan over the stovetop.

Either you want an open plan or you don't. There's no right or wrong to that choice, but go with the one that fits your actual needs, rather that building what's trendy and then trying to retrofit it to perform like the other type.

You can smell a cookie baking.........or a fish frying, (fan or no fan)......at the front door, no matter the walls. . Pick the way you want to live.