Can a platoon sgt tell a female soldier that she is required to wear a bra when in civilians?

You mention overseas deployment. The regulation references civilian attire, deployments can also have restrictions based on the are you are deployed in. However, each case requires written guidance. If the deployment for some political or other reason calls for more restrictive measures then that would justify a written directive/policy stating these restrictions and why. If they press request to speak with the CSM.

Based on my experience of females in the military, I would bet actual money that there is more to this. For example, maybe the supervisor has not much need to ever wear a bra, and the subordinate has more of a need, or, for some other reason probably known only to her, the boss wants to fuck with the SPC. Maybe, literally.

I have seen both of those circumstances play out during my time in service. I have had to move women away from each other because if I didn't, it would be perpetual conflict until I had to do something bad to the junior because the senior just would not quit unmercifully singling out the junior to take shit on all occasions..

I had a SrA with tears in her eyes offer me a BJ to get her away from her lesbian (she said, IDK) supervisor. I didn't take her offer, I couldn't have. Laugh if you want, but it was pathetic, it would have been like taking advantage of a blind deaf cripple, and I would have had to face her every day.

This was in the '80's, women had just come into my AFSC (MOS) and the woman was afraid all the other females would turn on her for making them look bad in their newly opened AFSC if she outed the boss's advances. I told my boss my suspicions, though not about the offered sexual favor, nor the lesbian advances, and got the subordinate moved.

There would have been soooo much shit if I had brought up the lesbian advances, and the supervisor would have been kicked out, the subordinate's career crippled and every female in the unit would have turned on her, and maybe, the shit explosion would have fallen all over me.

If the USAF wanted to put me in an untenable position, I felt no need to throw away my career, job, money, and life style.

A female sending a subordinate male to tell his subordinate female this shit is just asking for a complaint of almost any kind, substantiated or not, and reeks of ass-holyness. Maybe it's the male subordinate who is the SPC's boss whom the supervisor is messing with.

Maaybe, she thinks there is something going on between her male subordinate and the female SPC, and this is her sending a message to stop without actually acknowledging the relationship and therefore having to take action.

What I have written is based on my true experience of being in both the USAF Fire Department and the Security Police when they at different times during my career allowed females to enter.

Let the accusations of sexism, misogyny, probably somehow racism and definitely homophobia, and general hatred begin. Oh, and you can virtue signal at this point too, if you desire, tell me how wrong I am and how much better you would have done. If you like. Maybe not, here.

You’re on rotation. Not at home. Put on a bra. Or at least wear a sports bra when out of your room.

First let me say my experience in the Air Force might not be useful for someone in the Army. After reading more answers to this question than I could imagine might be appropriate I am left feeling that the order you received was not delivered very well. In my experience such an order would be accompanied with an explanation of why it was necessary. Indeed, in my 8 years of active duty in the USAF I never received a direct order. Instead what I received was statements about what my superior would like and that was enough for me to do what he wanted (there weren't any females in my chain of command). After my first three years on active duty all my immediate supervisors were commissioned officers ranging from captain to major. I would feel comfortable asking any of them for an explanation of this kind of order if I ever got one. I am sure the response from any of them would be a clear explanation of the reason behind this or any other order. In your case I would think going up your chain of command far enough to get an explanation would be within your rights as a human being. I would expect the explanation to be that local standards in your overseas location dictated this behavior to be consistent with other women there.

Curious to know how it all turned out.
Under stateside conditions, when you're off duty that's the end of the day and you're free to roam about as you please.
However, the question was posted for during a rotation overseas. With the effect of GO1 being active all the time, I believe that the PSG is within their ability to address the wearing or not wearing of a bra while 'off duty' unless it's solely while in your quarters. Whether it's for interacting with local nationals or just decency is something to be addressed with the PSG who brought up the issue; they should be able to say exactly why their expectation is to wear a bra.
I believe while in Iraq the clothing requirement while off duty if we were going to interact with locals involved pants. Men and women shouldn't show leg because it's not part of the culture. Just little additions to GO1 as we went along on top of the no drugs, sexual contact with locals, no proselytizing, no fun anywhere, etc.

For the most part, yes your leadership can.
However, the male team leader would have been better off being accompanied by either the female PSG or another female NCO. The female NCO basically would be back up to the male ( reinforce the regs and local guidance) and frankly to cover the male NCOs butt from a SHARP incident. In the event of no other female leadership being handy then at least another NCO.
Yes it is an intrusive issue, but the commanders in the Army can set policies and the NCOs enforce them, often including "intent".
If it turns out the male team leader acted on his own ( suspicious in my mind If he did) or if you think you're singled out for some reason then talk to someone ( PSG, 1SG, Chaplain, SHARP, etc. You've been to at least a couple of classes )

To leaders reading this, I'm not saying a male leader should have a female present for every conversation. But issues as personal as this, some other witness should be present. Vice versa if a female has to correct a male ( ie maybe he like to wear shorts that are too short). Immediate on the spot is one thing, but a correction of a pattern is another.

When I was in the Army, they issued us all the clothing we should need to accomplish our assigned tasks. Did the Army issue you bras? If they did then it would be reasonable to expect that you would wear them, if not than I think you can assume the appropriate response.

If you can notice you're not wearing a bra i can guarantee you can see nipple at times. Every branch has civilian regulations we must follow, which were made up in the 1950's. Guys probably love that you don't. She is either looking out for you or jealous of the attention you get from it.

No

It’s an image you project as a Soldier. If you have to be told then you probably don’t get it. SMH