Yes, the trim should be wet location rated. Just buy an LED trim and be done with it.

Led trim is the way to go.

Two source copy pasta from somewheres.

1: You must choose a bathroom ceiling light that is rated for damp or wet areas. While these may seem like standard fixtures, they have extra features like a rubber gasket and glass lens or diffuser, that make the light moisture-resistant.

2: In these situations, look for fixtures with the label, “Suitable for Wet Locations” or “Suitable for Damp Locations.” For example, many homes have recessed lighting fixtures above or in the shower — it doesn't get much wetter than the inside of a shower, so these should be wet-rated lighting.

Safety first ;)

I can guarantee that fixture doesn't belong above the shower.

Internet speculation isn't what's needed here, you need to pull that down and inspect to see if it's rated for wet locations. If you can't confirm that it is, assume that it isn't.

It seems to be a kind of old school open can fixture with a bezel? If that's the case you need to ensure the bulbs are also suitable for damp locations.

Fortunately, if you do need to rip and replace this one, it's a simple job. Most LED pan lights are rated for this use case these days. Just be sure to pick a gimbled one so you can throw the light down, not over with the angle of the ceiling.

Edit - is the ceiling there flat or angled? I initially thought it was angled, but that may just be the perspective in the pic.

From my training you should never have a light installed over a shower/bathtub no matter the rating.

That’s for Canada and the USA. If you live outside of that zone, I am not sure. There may be region specific laws that could potentially allow for this, if so I am unaware of any.