Just make sure you take into account how the door is hinged and what clearance it needs to open fully. Some cabinets designed for surface-mounting may not open properly when recessed.

We're doing a medicine cabinet perpendicular to the sink (technically a 6' T x ~ 20 W cab that projects 6" into the room -- we can't recess because of pocket doors). It's a variation on a newer-construction solution that works for our old house space. [Seriously, I can't think of a 1980s+ typical development house that DOESN'T have that set up!] So obviously I think that solution is fine; it's never bothered me when visiting people and I don't think it's any more inconvenient than moving/leaning over to access a cab above a toilet...and I've had THAT set up in another bath for 6 years.

That's pretty much the worst place you could have a medicine cabinet. Medicine stability data is generally obtained at room temperature (60-70 degrees) and low hunidity. "Accelerated" stability is obtained at 90+ degrees and high humidity (just what you have in Florida). Most medicines are not particularly stable under those conditions so I suggest you fine a different place to store them.

Not sure if Houzz will let me post a link but I’ll try: https://www.rejuvenation.com/products/mendenhall-medicine-cabinet/ Or search for Rejuvenation medicine cabinet—they make several variations, and all but one are the same dimensions. (Wright is the one that’s different, I think.) We have two (one purchased for a new bathroom last year and the other for our existing bath 9+ years ago) and really like them; initially got one from another store and returned it because the quality was disappointing. We were DIYing the first installation and building it from scratch was well beyond our skillsets, but this was pretty simple. We are in a very high cost labor area so would have paid considerably more to have a carpenter build one. YMMV if you’re in a lower cost area.