I would keep cabinetry it's own colour scheme and wainscoting white. Although the cabinetry on the right side of the fireplace can be painted to match your kitchen. Maybe removing the mirrors is in the budget?

I kind of love the mirrors in the cabinetry. I think all guests to your living room should be offered a smoking jacket and a cigar, please. That paneling and cabinetry should be given a retro vintage feature--it is a statement, and I think you can have a lot of fun with it if you lean into it.

Are the kitchen cabinets going to be green? Since the cabinet styles are different, they don't need to be (and probably shouldn't be) the same color. I would pick another color for the living room. What color and material are the floors?

I wouldn't change the colour of the paneling. It's what gives your house its character, and while it may look a bit dated as is, it also has a classic English smoking jacket vibe to it (as Muriel said). With just a few minor changes I think it could be updated while still being true its intent. I like the wood brought in in the blue kitchen photo, but I think green works better for this space and ties in with the stone? fireplace surround.

With a kitchen like this, but obviously with a more open floorplan:

Kitchen · More Info

I like the blue-green as well. It isn't as warm, but it's more modern and almost slightly beachy. I think the navy is too dark unless you do end up painting the woodwork white. You might find, though, that the cabinets may still look just as dated if not more if you paint them. It's not just the colour, but the shape, particularly of the lower cabinets, that gives that look of being dated. If you're keeping that wall, you might as well make it look intentional and play into it.

Was also going to suggest keeping the LR in natural wood, but I love the idea of painting the ceiling to go with your kitchen cabinetry!!!

Just some visuals...

Or perhaps your cabinet maker could replicate the paneling in the kitchen, above the stove or island.