Be creative in small spaces. Just think everything through in terms of sizes and positions.

It is definitely not weird! I love a floating vanity, particularly in small spaces. And if you're not looking to break the bank, it can also be quite economical as you can avoid the expense of a vanity.

Looks cool. I would like it, but people who are claustrophobic or wheelchair bound might have issues with it.

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The ones that Beverly shared are nice, but not really the style I'm looking for. I would still like some storage space plus a flat one-piece sink instead of the bowl style sink.

To Sissyphys's point, the space is actually a bit under 36", so I think if I buy anything that's "standard", I would have to shave off a bit of the sink to make it fit. And yes, I'll have to double check space with drawers.

I did a bathroom for a client that wanted to use this floating white vanity and a remnant piece of quartz from his kitchen

I never got a fully completed pic, . the walls weren't yet painted, and the wood in the niche wasn't completed. but you get the idea

His was exactly 36"

don't know what your style is, but you could do just about anything

Lowes has this in a 36" floating style. you could install something below, or even a toe kick if you like. See other pictures.

I don't really care for this vanity though. it's cheaply made (notice the rails and stiles)

You could modify that style to look like this in the alcove:

doesn't have to be floating

I am also doing a floating vanity in an alcove. I purchased a Godmorgon Vanity from Ikea and drawer fronts in Walnut from Semihandmade. I also purchased walnut filler for each side of the vanity to fill in the space. I am going to purchase a quartz countertop for the vanity and will have a vessel sink.