How to correctly test a 4-channel Logic Level Converter?
Thanks for the photos.

The updated photos of the converter's PCB don't reveal any concerns.

However looking at the photo of your breadboard, a problem is clear: You haven't soldered the header pins onto the logic-level converter.



That will lead to a variety of potential problems, depending on which connections made good-enough contact, and which do not.

Please solder the header pins to the converter board, re-test, and report back.