Ok, so if it's only 3" thick, it's not a normal wall. If it's crumbly-masonry that's falling out then I would assume some sort of plaster & lathe, but it doesn't sound that straightforward by what you describe. You're hanging a pot-holder on it? Hold all of your pots and the holder itself in one hand; I bet it's too heavy for anything less than lag screws/ lag bolts. You're not just worried about shear-weight, you're worried about pull-force because the center of gravity is going to be ~5" out from the wall.

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>I was thinking of just sticking a lag shield into it and using the lag screws that came with the pot rack.

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Yeah that sounds like a plan. 3" thick wall is skinny af, so just bypass whatever weirdness Previous Homeowner did.