Look at the brick. It should say what it converts the 120v to. Something like 12vdc 1a or 5vdc 2a.

Find a power supply with terminal screw, spring, or wire ends that converts 120v to the same thing. like this

Thanks! Ok, that was super helpful... In that case, maybe you are right and I shouldn't play with high voltage either.

So let's say I use the bulbs you linked:

I could still use these lamp sockets (so that I can switch them out easily if they ever need replacing, or I could solder and heat shrink, like you mentioned), extended with this pigtail wire if necessary, solder and heat shrink them together to splice them in line, ending with these pigtail to barrel plug wires, so that I can then use this inline dimmer, and then since the bulbs are 3W, this AC110V>DC12V adapter for up to 15W should work, no? Then connect the two AC wires from the adapter to the two wires coming from my ceiling and the ground wire to a metal part of the lamp.

Sound right?

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Again, really appreciate you breaking this down!