I didn't read all of the replies, but I have a quick solution to offer. Instead of putting something IN the wall you could frame up a narrow pony wall type of situation and create a ledge the full length of that back wall. Like the Zerby's bathroom at chezerby.com. We have a narrow ledge like this on the back wall of our shower and I think it's only 2.5 inches deep and holds all our costco size things just fine.
ETA: I'd put the ledge at about 36" or whatever height is comfortable to reach from seated in the tub as well as standing in the shower.
ETAA: If you think you'll be living here indefinitely or if you have aging guests, you might take this opportunity to add blocking for grab bars.
Q
Could do just half wall of the vanity side
Q