I think you need to share the wood flooring you seem to be set on that will IMO drive the issue of apinting the wood.

Not a Pro and not a wood lover. IMO the stained boards look good because the plain carpeting gives the eye "rest and contrast". Waiting to see your choice of wood flooring.

I would paint it in a heartbeat.

oh my goodness, I absolutely love your bead board! It is beautiful, especially because of the way the white "frames" and cieling set it off and make it look more modern. I know I have saved some pictures with wood walls and floors. I will see if I can find them and post them here.

For now, post a picture of the floor you want and maybe someone can Photoshop it in for you!

Here is a link to a Pinterest board I made of wood panel walls.
https://pin.it/hbsvwndgtnoc5b

Most of these rooms have lots of white to balance the wood and give your eyes a break and a good amount of color to brighten things up. Furnishings tend to be either vintage or mid-mod. There are a couple with dark floors below.

Here's a visualizer with the flooring I like plugged into both spaces. The 1998 parts of the house could really use the warmth of this flooring - but it's a lot of wood in the living room...even by adding a rug, I'm a bit overwhelmed.

what if you paint your baseboard in the living room white like the window trim? It will provide a break between the wall and flooring.

Not a Pro.

Love the beadboard, I would not cover it and yes the floor may not look like a great match, but area rugs should take care of that and break up the wood throughout.

I also think your wall decor should be changed out. You need much larger lighter art. Take away all the little art and update the walls. No mirrors, they just reflect more wood walls.

I can't believe I'm saying this -- but my opinion is, don't paint the beadboard. totally agree with the 2 posts above, paint the baseboard white to match the window trim & once you put a few rugs down, it won't be so "woody".

My first inclination is to say new wood flooring with the existing beadboard would be overkill but if you are going for a truly vintage look then maybe not. I've seen photos of homes from the late 1800' that feature pretty much all wood floors, walls and ceilings. I don't think all wood rooms are conducive to modern living but, one again, if you are going for a vintage look it might work. If you are going truly vintage I wouldn't paint the beadboard. Also, if you ever want to strip the paint and return back to stained wood finished it will be quite a job. Good luck with your decision!

Not a Pro.

This may not be your style of decor, but take a look at this inspiration. They seem to get the look they wanted for their home without touching the wood work.

Inspiration:

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I would be inclined to keep it! I’m so curious about the exterior of your home too.