The cheap stuff usually have the certification labels printed on them, but a cursory look inside usually shows breaches if you know what to look for (like we have had stuff from China where the ground wire wasn't connected to anything, but even if that's right there are things like just not having enough clearance between mains and isolated DC in power supplies etc.). So they are definitely not actually certified, they just slap the labels on anyway.

Of course, there is a rising group of actually really high-quality native brands starting to come out of China - Anker were an early one of these, Xiaomi is a massive one, UGreen is really popular on Amazon etc. These kind of brands actually will be properly certified and are scary good for how cheap they are. So it's changing a lot.

Definitely not UL (if we're talking about the $300 inverters on Amazon or AliExpress from companies like Anenji)