It’s not an appropriate design if it results in your vanity getting wet. Period. You either need a curtain or door for the shower, or you need a smaller vanity that won’t be so close to the shower, or you need a complete lately different design. Wetrooms must contain waterproof elements, not water resistant.

Glaze has no place to hang up on a slab door. Most manufacturers won’t do slab or shaker doors with glazing for that reason. Glaze is supposed to hang up in the details, and you need a door with some of those details to make it show. A floating vanity that’s mounted at only 6” off the floor is doable, but it’s more difficult to clean under than one mounted the more traditional 15” off the floor. The traditional height of floating vanities is 18”H and 21” H. Have you lived with a vessel sink before? They are gorgeous! But they have more water on the counter and more water running off of the counter than an undermount sink. They’re more work to clean and maintain than an undermount. I just want to make sure you have considered all of that extra work before the decision finalization. :-)

I'm not sure white would neccessarily make it better, I think the current stain works well as a transition between wall color and tile color. (I'd prefer either much warmer tone for wall color, or something more intense..because of the tiles. But the current paint doesn't look bad, and if you love it-I think it's important for it to continue to work nicely, and I think stain does the job in connecting these two). It also provides nice contrast with the current countertop. Would be harder to get this contrast with white paint. So I'd rather restore it I guess. Having said that-the mirror looks pretty traditional, which I love, but you might not, and the lights are more contemporary-leaning..so if you want to downplay this traditional look, I think white paint will help with that. So it depends. I think it's overall a nice bathroom, and whatever direction you decide to take-with nice accessories, both will work. No, you wouldn't be able to go back to stain after you paint, not from what I know at least. I also agree with eld about longevity of stained vs painted..painted has to be babied more, in general. Even though if you paint yourself you can always touch it up.

As someone who moved into a home with a bathroom with stark white countertops (thankfully not in our primary bath), I think they aren't used as often because they show every smudge of toothpaste, hair clippings, mascara, etc - and your eye goes right to the mess. It's enough to drive you bonkers. At least with a little veining or movement, it distracts from the normal everyday stuff and prevents you from wiping the countertop multiple times each day. I've put in marble countertops in otherwise neutral or B&W baths before - it's actually a pretty traditional/classic look. I do like where you're going with putting some wood in there - it will add some nice warmth. Also, I think some places (although not Pottery Barn perhaps) allow you to order the vanity with no top. If you find one that is otherwise perfect, check the item options to see if that's a possibility. I'm very anti the afterthought 4 inch backsplash piece that comes with most vanities (I prefer to tile behind the sink), so I have taken that route in the past. That said, I would second the suggestion to consult with a custom cabinet maker (especially if the only thing stopping you is sample sizes - I'd imagine they could give you an entire drawer front if you really needed it!). The price is often negligible, and it provides you with more control over the numerous options that are clearly very important to you (I say that in solidarity as someone who is known for refusal to accept limited options!). The other benefit of going custom is sizing - a custom cabinet maker can build a unit to any width, so you can maximize the storage and counters to your space. They could also give you the two drawer/open shelf combination you're describing (although keep in mind those drawers may be limited to allow for plumbing for the sink). Another random source is Etsy - there are a few sellers who make vanities out of repurposed cabinets that might appeal to you. Check out CuratedHavenDesigns (I've had their "ornate bathroom vanity" listing saved for a while now - if only I had somewhere to put it).