AC to DC transformer for LED

It makes sense - look for "low voltage LED Lighting" to see what's available, or slide on over to Electronics to build your own.

Dimmable LED bulbs are those with drivers built-in that are "dimmable" - if just running controlled current to LEDs, they are all "Dimmable" (lower current, lower light) so, no, you don't want an LED described as "Dimmable" (nor one described as 12V, probably - a "bare" LED with no other parts attached is best when you are going to feed it controlled current.) If you purchase a "12V dimmer" pre-made, follow the dimmer-maker's suggestions on types of LEDs to attach to it.

LEDs are current devices, so controlling the current will give highly consistent light output (controlling the voltage, less so)

Some are. You can also get transformers designed to mount into a 1/2” knockout in a junction box. The transformer proper sits outside the box. You can also find transformers which sit on the outside of a metal box cover. These are very common in 24VAC.

These are typically true transformers. You may be using the word "transformer" loosely to mean any low voltage power supply. That may be a bit harder to find.

Any device you put on 120V power should be UL listed for the purpose, or inside a listed metal enclosure.

Another option, if there is a metal fixture involved, is to mount the power unit inside the fixture.

You do need to watch out for box fill limitations. Don't overstuff the box.