A satin shirt suits anyone who wants a plain top to look like more effort than it was, the sort of thing that makes jeans look like a decision rather than a default. It's particularly good if you like a bit of shine without going full party fabric. Where it gets tricky is on anyone who sweats easily or moves around a lot during the day, because satin shows every damp patch and clings in a way cotton never would, so if you're on your feet all day or prone to overheating in meetings, it's worth thinking twice.
It's the wrong choice for anywhere you need to look polished and also do physical things. Satin creases if you sit in it wrong, it shows pin marks from a bra strap, and it is not forgiving of a big lunch the way a looser cotton shirt is. It also isn't a great layering piece, because anything on top slides straight off that slippery surface, and anything underneath shows through if the fabric is thin, which a lot of the cheaper ones are. I've worn one under a blazer and spent the whole day hoiking the shirt back into place every time I moved my arm.
On fit, go up a size if you're between two, because satin has very little give and a tight satin shirt pulls across the back and gapes at the bust in a way that looks like a mistake rather than a style choice. Check the sleeve length properly, satin shirts often come with a longer cuff than you'd expect and it can sit past the wrist bone rather than at it, which looks sloppy rather than relaxed. The collar is worth checking too, a soft satin collar that's cut badly will just flop rather than sit with any structure.
The difference between a good one and a disappointing one is mostly in the weight and the weave. A proper silk or a heavier satin weave with some substance to it drapes rather than clings, and it doesn't go see through under shop lighting. Cheaper polyester satins feel thin and a bit plasticky, and they pill under the arms within a few washes. Look at the buttons too, mother of pearl or a proper resin button feels different to a flat plastic one that catches on itself. French seams or a neat flat seam at the side will stop it twisting when you wash it.
It gets better with wear in some ways, the stiffness in a new satin shirt softens after a few washes and it starts to move properly rather than feeling like it's wearing you. But it does lose some of that initial shine over time, and a satin shirt that's had a hard life looks tired rather than characterful, it just looks like it needs replacing.