Ok, on the RGB Keypad there are those two rows of solder pads, one down each side of the Pico. They are each a single row of 20. As are those headers I linked too. I couldn’t find a non stacking version of them.
One option is to solder those headers to the keypad circuit board, then cut off the excess male pin lengths. Female side up would be the way I’d go. You can then plug in male jumper leads. It’s functional, might not be so good to look at with the jumpers plugged into them.
You could solder them to a Pico, and then plug that into the RGB keypad, but why bother? IMHO, it will look nicer the other way.
This, for me anyway, is one of the more frustrating parts of building something from bits and bytes. Making it functional and look good.
I have on occasion used these Perma Proto Boards. Quite often actually, with Pi’s and Pico’s.
Search - Pimoroni
Used one of these on my last build.
Pico Proto PCB (pimoroni.com)