If a STEM PhD holder applies for a Master's in another STEM major, would this be an advantage or disadvantage in the eye of the admission committee?
If you ever want to leave academia, it could be seen as a disadvantage. It suggests you are a "perpetual student" rather than someone who actually wants to do some (real-world) work.
The main point of a PhD is not that you learned some (random) snippet of new information while doing it, but that you demonstrated you can learn new stuff on your own with minimal supervision.
That is what you should expect to be doing for the rest of your working life, either inside or outside academia, but expecting to keep getting more "awards" for doing that is rather like a kid in school expecting to get another gold star for every good piece of homework they turn in - most people grow out of it.
Sorry, but you walked into that joke. Actually, such an application would occur so infrequently that it might result in a few chuckles. But I don't think it would have a lot of effect. But certainly not a big advantage.
In fact, people, including myself, will wonder why a person would bother. After all, the applicant can study and learn effectively and evidenced by the doctorate, so what is the need of a formal program. It might be a disadvantage in some places where the available slots are limited and people would feel they should be given to someone who needs the training more.
On the other hand, if a lab needs particular skills that you have, they might be interested, just for that.
Thus, it is impossible to say in general as local needs/beliefs will dominate such a situation.
Not a direct answer to your question, but a personal experience. I got a PhD in EE and am now one semester away from finishing my masters in CS. Three years after my PhD, I changed careers from EE research to a data science. My EE PhD provided me background in linear algebra, partial differential equations and numerical computations. The primary motivation for me going into MSCS was to develop intuition in certain areas which I wasn't exposed to, but became important in my new career: combinatorics, statistics, probabilistic modeling, optimization, operating/distributed systems, and computer networks to name a few. Following a masters curriculum guided me on what areas are (roughly) considered important and also brought a (forced) discipline to my studies.
If an application of MS followed by a PhD crossed my desk, I'd laud your discipline, but also probe on why you went that route. You need to have a good answer for that.
In terms of competency, I can't imagine why it would be seen as a disadvantage. If anything - it shows that you are capable of successfully completing an academic program.
The only scenario I could imagine where this may be an issue is if the Master's program is affiliated with some scholarship program, where the scholarship terms & conditions require that the applicant does not hold an advanced degree. If you're applying for a non-scholarship program then I can't imagine why they would reject your application - you are willing to pay good money and are likely to successfully graduate.
Another issue might be if you're applying to a STEM program that's very far from your PhD degree (say, from theoretical physics to zoology). If your bachelor's degree does not fit the prerequisites for the program you may have an issue, and the PhD won't help (but probably won't hurt).
Would not be any purpose of doing two different STEM MSc:s. After one you are supposed to be able to learn similar level stuff even faster on your own.
I could understand wanting to do an economy MSc to complement your STEM knowledge. Quite some people ending up as CEO or CTO of medium or large size firms seem to have double degrees: one in tech and one in econ.
It's a plus on the side of competency to complete it, but a concern on the side of whether you would actually enroll and finish the degree if you are accepted. But the school, year and discipline of the PhD, the school and discipline of the Master's, and why you are switching play hugely into it. Also, frankly, your standardized test scores and ability to fund your own education, just like anybody else. I'd recommend talking to an admissions person at the school you are considering, as well as a hiring manager in the field you are considering. (BTW, I'm a PhD in Management Information Systems who was in academia for several years but have spent the last 12 years in industry.)