Help in finding a particular connector
That looks like an m3 or m2.5 broaching nut, but by the looks of it, it is not a solderable nut. It looks more like a press fit broaching nut, that is used for pressing into sheet metal or plastic. (you can tell by the corrugation on the sides which is typical of broaching nuts.)
A better way to do this is to use a solderable nut that is built for PCB's like these:
Some better options are listed here:
https://www.pemnet.com/fastening-products/fasteners-for-mounting-into-printed-circuit-boards-2/#
https://www.adafruit.com/product/4206
https://www.digikey.com/en/product-highlight/k/keystone/surface-mount-threaded-standoffs