UPDATE: I applied CAIG DeoxIT FaderLube D5 to the AN8008 rotary switch contacts and it's working great. It looks like any PPE fixes the copper leafs issue. Before, I'd tried cleaning with IPA and a soft scrub on the copper, then lube- which only works for a few weeks even in a dry workshop.
Before, I find an oxidized rotary switch gives bad, wandering readings on continuity/200R scale, or power cutting out. You'd have to do the ritual back and forth a few times to scrub off oxide, which also seems to make an offset potential which could be what that you are seeing.
This DMM chip set is kinda old, they have milked the cow for many years. It needs to advance from 8-bit clunker at 4MHz with a few KB OTP and few hundred bytes RAM. They can't keep adding features in assembly language, kinda tricky.