It picks up the PS2 in AV2 (with the typical red yellow white connections) though it still doesn’t display anything aside from the test screen regardless of the setting.
I do have the official SFC SCART cable for Super Famicom, and the SCART cable for the PC-Engine RX.
You should get a black and white noisy image with the yellow composite video cable connected to the green AV2 input. Can you try it on a monitor?
The official SFC RGB cable is JP21. Did you rewire it for SCART?