Here is how it leads into kitchen

the paper option sounds great. I would paint all the wainscotting and trim a color in the paper rather than leaving it white, it's a separate room, would be a real statement and the furniture would look lovely. You have to prep the walls for either installation, traditional or peel and stick for a professional finish.

Sounds like there are too many colors going on in the house and it will be difficult to have anything blending . There should be places for the eyes to rest . Find a vintage age style wallpaper from the age of the house and blend all that white wainscotting and trims too the background color of the paper ...but stay soft . Then follow with the same plan for the rest of the house . Maybe find a designer for consult or even a design stupent ...they need that for their postfolios , so they might be more affordable . Plan doing an idea board ...then you can see what will go together etc. Good Luck !

Blue is ususally a better color to use with cherry/mahogany furniture. Of course you can replace the paint with a wallpaper of your choosing.

Here is your room with a variety of wallpapers.

Frostbite is a nice neutral with warm and cool tones.

Our living room is a navy blue so I don’t know if that’s too much? I know there is a lot of color but I thought the frostbite would do a good job pulling in all the colors- teal, green, blue

Whether a wallpaper will be tacky or too much is a very personal choice.

If you are lucky to live in a major metropolitan area with a to-the-trade design center, then you have a lot more choices. Most of these design centers will allow you to walk around and take photos of the large wallpaper sample boards. They won't give out samples. Nothing like seeing a large sample of a wallpaper to get a feeling for the overall repeat and colors. A small sample just isn't the same. You can then order a sample online, to check the colors at home.

If no design center, then look for a good wallpaper store in your area.

PLEASE?

We aren't seeing the living room, the foyer, the library. the kitchen.....

Not every color need be in a paper to tie a palette together.

Show all the spaces? Thank you!

Your dining room seems quite traditional. Am thinking a William and Morris wallpaper might work quite well there. There a tons of patterns and colors that you could select from.

I need to see all the spaces and honestly you lost me at the teal cabinets . For sure get good quality wallpaper in this situation and IMO choose one that has all those colors in it to make this work . I think too many colors usually are hard to work with and honestly teal cabinets are odd in this mix.. I think seperate DRS can be quite different than other spaces but done thoughtfully to not make you crazy with just too much in the whole house.. The upholstery on the chairs seems an odd choice too.

Some visual with wallpaper