You are talking about the Pxx conector in the 3DS XL that retains the flex cable coming from the touch screen.
For the 3DS XL is has four differents : P10, P12, P13, and P17.
You can find it in ebay and some other on-line stores.
https://www.aliexpress.com/item/10pcs-Touch-Screen-Ribbon-Port-Socket-For-3DS-XL-Repair-4-Pin-Connector-P17-P12-P13/32762921830.html?spm=2114.40010308.4.36.jlaiAO
My advice buy at least 10 if having a regular solder and good soldering skills, because is quite easy to damage it.
Ideal fix is done with a microscope, heat station, and a lot of good flux.
Fixable but not easy.
Good luck,
Juan