That is called a junction box, not trim, that is not a "can.

look up "low profile" flushmounts

1. You could try installing a Halo SMD 4" fixture whose guts you push into the existing electrical box. Read the instructions carefully before considering this.
2. It appears you can remove the electrical box by loosening three screws. If this is the case, I'd do that, measure the diameter of the hole, and install a canless recessed light that fit in the hole. If you couldn't find a fixture whose trim would cover the old 3-screw mess, you could enlarge the hole and buy a fixture that fit the larger hole.

• 3-inch example
• 4-inch example

Do you have access from above? How many other appliances are on the same circuit? Is this box switched and do you know how to wire it for a switch? Are there other ceiling lights in the room? Is this in a place that one light would be sufficient?