Hello, here are some suggestions for choosing a wall colour.

For your cozy cottage type house, I think a cream that is not muddy would look very nice. I can see where you want to paint over the green. The green gives everything a drab look. Its not the green itself, that does that, its the shade of green, you have. Cream would be a good neutral as long as you pick one without a muddy look.

SW Repose Gray SW 1015, BM Abalone 2108-60, and BM Collingwood OC28

each compliment all the natural oak trim/floors you have.

While keeping it cozy and still freshen up the look. Sample a bit of each (in all light phases) and see what you think. Cheers to a fresh look in 2023!

I'd pick up a very light tone of the warmer stone that's in your fireplace. I happen to love Benjamin Moore's Sailcloth--it's a warm off-white that will brighten the space but still work well with all your wood trim.

SW Creamy, Alabaster, Greek Villa, Shoji White or Accessible Beige (their popular warm whites and AB is a little darker). Start sampling, you won't know until you try several things what you're going to like. It's hard to find one color that works in every room because northern light is so different than southern, etc. If you can't get one to work everywhere you can always paint bathrooms and bedrooms different colors. BM Sailcloth that Sabrina mentioned also looks like a good one to try. They have a selection of warm whites if you prefer that brand. Be sure to sample the color(s) on multiple walls, preferably against a white background so you're not distracted by how it looks against the existing color.