There are ways to do this but to answer your question, can you tell us more about why you would like to do this?

I would like to make a rectangular hole between 2 pads. The purpose is not electrical but a mechanical function. And I want them to be pads to be able to solder a PCB with another one while keeping the slot.

Do you want the pads to be through plated? So for each pad, you end up with a half-round pad on the top and bottom (and any inner layers if you have any) with a smaller radius through plated half-round hole on the inner edge of a rectangular hole in the inner region of the PCB?

Yes, that is the goal, is it possible?