A coat of varnish will make the colors pop and darken the wood a bit. More brown, less grey depending on its condition.
It also discourages bugs from eating it.
It may not be to your liking so test on another bit of the same wood.
I still do rustic projects a few times a year and they all get that wet look with varnish.
Latest are a horseshoe coat tree on a hardwood tree trunk post and a wall hanger horseshoe hook on weathered wood.
Sorry, no pics as I cannot reduce photo size on my phones.