Oh, here's a link to the Silver Sage look

Here is a link that might be useful: Silver Sage Cabinets

I see no problem with having the kitchen painted and the rest of the house trim in wood. I would, in fact, be happier to see the kitchen painted than have the mismatch of woods. I don't mind different woods, and don't mind certain colors of oak, but 'close, but not quite' (both woods in the medium range, but with different color undertones) would bother me, I think. In your case, from looking at the photos, anyway, I wouldn't save out any of the oak unless you really want to...Or you could consider staining some of the oak if you still want some wood in the kitchen so it has more contrast with the other wood.

Paint away... I agree, better to have painted with wood, than too many woods that are "close, but not quite".

I wouldn't leave any oak cabinets the current color if you paint some silver sage. I don't think the silver sage color goes with the yellow oak. Maybe the right shade of creamy white would look OK with the existing oak finish.

For a wood finish to go with silver sage paint, I'd experiment with espresso. Or, you could also strip off the current finish, which I'm pretty sure is a yellow lacquer, quite easily, brush on a solution of baking soda for a driftwood-like color that would look great with the silver sage.

I have very similar oak cabinets and have played around with different finishes on them. At first I thought it would be easier to paint than to strip and refinish -- but it's not. Not if you are picky about the paint finish anyway.

I agree. If the picture tones are accurate, one is yellow and the other pink. Expresso or driftwood colors would go much better with the rose tones, unless it's too busy to introduce another color in addition to paint. The grey sounds like it would warm up and go with stainless steel, while calming the paint if you want that. good luck.