I would double check with owners that they are OK with you painting paneling. Sometimes when people say you can decorate any way you want, they’re not remotely thinking of altering paneling. Be 100% sure, maybe even in writing, so your security deposit is not held hostage over this.

cannot imagine a gray wash lightening the space, which is what I’m assuming you want to achieve.

^Agree with bossyvossy on both counts. Even if the landlord says yes, get permission in writing as an addendum to your lease before you do anything. Most leases I see say no alterations are allowed. I'm a Realtor.

As to the graywash, can you show a pic of your inspiration of a barnboard graywash over dark panelling?

You probably need to seal it first with a stain blocking primer like Kilz or BIN. You can then paint it with regular latex paint, at least that’s how I did it years ago. I doubt you can get it to look like barnboard because it will not have the texture of real wood. If you want to lighten up, I’d just paint it white or cream and leave it at that.

Assume the paneling has vertical ridges, mimicking boards...? If you are not bothered by those and just want a lighter brighter look, there are heavy duty primers that will cover any gloss there is and give a good surface for any paint. We did this back in the 80s, liked the reult and never had a second thought. Just ask a good paint store (pref not big box), they know their business.