Get some advice on building and lighting appropriate for “wet areas”, ie bathroom/laundry/kitchen that have different legal requirements for safety.
You would need to use an enclosure/sealant that is sealed against water immersion. Usually IP65 or IP66/IP67
Even if it’s in the ceiling or in the shower itself, water tends to attract to metal in regular humidity, excess humidity can cause water to pool inside conduits and inside containers, hence immersion prevention.
Which usually means it has to be sealed against any gas or pressure difference, so air can’t get in or out through vents or gaps. This also requires a solid heatsink design to mitigate expansion or overheating in high ambient conditions, ie placing lights near heat lamps or near hot water pipes, insulation, etc.
And you would also likely need to insulate high voltage wires that are outside/above the bathroom ie transformer and control modules, etc in a box that can be sealed with silicone/rubber grommets, sic. Especially if it’s in a cupboard or cabinet that is bathroom rated.
Outdoor lights can sometimes be used in a bathroom too, which may be cheaper/uglier.
Talk to a bathroom specialist about modified or adding lighting, they will probably make or use appropriate or approved enclosures and sealed conduit that can block dust and water, including sealing against immersion in water, not just droplets.
(Eg cleaning with detergents and solvents, caustics and bathroom products)
If you DIY this, you would be in a liability situation with the down lights because they aren’t low voltage or sealed.
It may be possible to use 120/240v globes ie GU10/BR30 in a sealed box, as long as the enclosure is approved for bathroom and immersion.
LED strips could be put into an enclosure/sleeve or conduit made of silicone with a diffuser/glossy layer to avoid cleaning caustics or soaps breaking down the enclosure / tubing.
Excess humidity will collect on the exposed circuits and chips/tracks and cause rust/corrosion. More so because it’s flexible, and because it’s often exposed to humidity and heat.
Even if the fan is always on, and there’s plastic insulation, a small fracture or exposure is possible, and cause the strip to dim, or flicker, or just stop working and cause a short. With the low voltages, fire isn’t a huge problem, but the transformer is still attached and nearby which could be a fire hazard (sic).
In cabinet transformers and any disconnects or plugs may also need to be sealed, silicone sealant and a sealed enclosure for any of the exposed strips because moisture beyond ambient levels can and will cause corrosion to the tracks on the strip.