We should ask ourselves "how much privacy is there on a modern-day military ship".
The fact is that the close quarters required for any ship basically removes nearly all privacy for everyone on board but the senior officers. While in the STNG universe, the ships are stupdendously spacious, I have always wondered how they managed to pull that off. The physics of carting around extra space for shnicks and giggles, plus the fact that any military ship would require some measure of agility (or at the very least, more agility than the next ship), usually means that you can expect any spacefaring vessel to have all the space of a modern-day submarine, except probably less. But on STNG, we have an amount of personal space that would be embarrassing on a modern-day cruise ship. While technically this is in line with the narrative that the STNG universe has an epic amount of energy to play with, it's still kind of over-the-top. For all intents and purposes, this can only be explained by breaking the fourth wall (and has a whole lot to do with that fourth wall, too, and the camera crew that occupies it).
But hey, I digress. The fact is that if a Galaxy-class starship is remotely comparable to say, a modern-day battleship or even an aircraft carrier, you would expect the enlisted men to have exactly no privacy, except maybe when they're in the shower for the 10 minutes they're allocated every day. You could expect their "personal space" to be roughly a 2x3x3 foot locker, without even their own personal bunk, instead sharing it with someone else when they're not in the process of occupying it. The junior officers would have marginally more privacy, "only" bunking two-per-room, and not hot-bunking. The Ship's captain and second-in-command would have quarters slightly larger than your desk at work, but they would have actual privacy within those quarters. They wouldn't be shared with anyone else. At the same time, everyone is still sharing the same small set of washrooms, even the captain.
This extreme lack of personal space (or any space at all, really), combined with the fact that you're "on duty" pretty much the entire time you're deployed, lends itself to the fact that you'd basically have no real privacy except for what goes on in your head or back at home. I personally can't comprehend how it could be any other way, since everyone is always either working, studying, or sleeping, and there's hardly any space dedicated to anything beyond those three tasks. The only time that someone wouldn't already know exactly where you are by your physical presence would be if you'd somehow managed to escape into the dead space between bulkheads. Having a tracking chip on your person at all times would be barely necessary at all.