What does the rest of your house look like?

Looks to me like you have stains, paint and nails to deal with andc it looks rouggh. If Im wrong and the surface is fine, then you dont need to seal it. It's been just fine unsealed for decades. Of course, if you leave it as is, you can axlways decide to cover it again later

I would like it painted, but I’m not sure it would serve its purpose, if it’s good enough to leave exposed. What I would like to seal are the big gaps between each plank. What can I use for that?

ShadywillowFarm it’s drywall. We only would do the living room this way.

Pigmented shellac (Zinsser's BIN in the red can) to seal. Knots will need to be double or triple coated with BIN. Prevents tannin bleed.

Caulk is about the only option for filling the gaps. Or use battens to cover.

I suspect that you are not going to like the results.

I agree with sacking. These boards were never meant to be seen.

Sheetrock.

I agree with those above. They will never look decent. They were not quality lumber to begin with, and were never meant to be exposed. They dont really look like shiplap either, they look like old boards that were nailed on for sheathing, and meant to be hidden. Take them off, and save them, and maybe you can find something else to use them for.

OP, I meant wrt your style. As others have pointed out, those boards are rough, and may not work with the style of the rest of your house. If you are rustic, vintage, shabby chic, you might be able to do something and make it work. If your style is cleaner or more modern, it could be tough to wok them in.

I see a tobacco basket on the far wall, so I'm guessing OP's style is country/rustic. If I ran into this situation and decided that I wanted to keep the wood exposed, I wouldn't paint it and I definitely wouldn't try to fill between the boards -- but that's me. It would actually make a great spot for me to hang/store things. lol!

Thank you everyone!

I have used 1x6 pine boards for faux shiplap and I love the look. The boards are not finish grade, meaning there are knots, some rough texture. I personally like the look you have and would go for it. Worse case, you dont like it and drywall over it.

Attached are a couple photos of my faux shiplap

For whatever reason, the bottom photos is not a true representation. The lines go all the way across and are not broken up like shown in the photo.