I like wood ceiling too and had them in all the rooms of my lakehouse but last summer we decided to paint all the wood and now I LOVE the painted wood. It still reads like wood but sooo cheery and light. We did it as the house is in Maine. I longed for more light in the winter (the few times I go up) but in your case the room is full of light so you could go either way. If your furnishings are going to be similar to the rest of the items you showed then you could go with a stain and add more warmth to the room. Sometimes the eye needs a resting place from the bright sun and that ceiling would be a show stopper if it were stained. I wouldn't go dark with the stain but more of a medium to light shade. Then I'd add some items in the same tone in the room to pull it all together. It's a wonderful sunroom, sigh.

IMO blue/ grays are hard to work with if i have a client that has to paint before a house is completed i highly reccomend a pale grayed green it is much more neutral than gray and seems to work with everything. Sea Salt from Sherwin Williams is a good color it is not the same as BM sea salt.

Ash being a light wood but can be hard to stain in a darker stain since it's such a dense wood - I would consider staining with Minwax English Chestnut # 233 add coats until it gets dark enough to match adjacent wood stain , also consider a very flat sealer ( such as tung oil or satin poly no shine is important against the flat finish of brick

@hallettco and @lisedv -I'm totally down for a black fence!! Our roof is black and our front door is black, so I think it might be nice to have the fence tie into those elements... I'd just need to convince my husband, who is very much not into the idea. As a compromise, I'm debating the idea of testing out more of a dark brown (ideally with cool tones since our house color is on the cooler side... maybe Cordovan Brown by Behr?) since that might still provide contrast with the house without making my husband sad about the fence color haha. You can't see our fence from the front of the house because the fence is set back, but here's the front for reference!