I am making a PCB, where I want to integrate the possibility of adding another PCB module to it that would handle the Ethernet interface mounted on the main PCB. I was looking for connectors or a connection system, but having no experience in this I would like some advice from the community. The requirement I have is that the module should be as close as possible to the main PCB.

 

Look into stackable headers.

 

What to use depends on the signal speeds and power requirements. There are a large number of options.
https://www.te.com/usa-en/products/connectors/pcb-connectors/board-to-board-connectors.html