Header connector for mounting in the PCB slot, does such thing exist?

connectors should definitely use plated slots rather than circular holes PTH slots are most often used in component footprints, and most PCB layout

2 socket for your expansion slot Just pointing out it could cause issues in the slot or device from PCB flex so be a little cautious!

pcb slot connector Slot, ; PCB edge connector slot 2*13 pins; Plating tin; Black; Packing with tray; Specifications: Voltage rating: 50V ACDC; Current rating: ACDC

slot machine tattoo flash Product Name: Edge Connector · Series: 805; Gender: Female; Pin Number: 36; Each Pin Width: 2mm · Row Number: 2; Pitch: ''; Material: Plastic