Note that "according to the bag" is very different from "according to your municipality"; my understanding is that most places actually can't handle them, and they might need to divert your compost to the landfill if it has too much of those plastic bags. They can be composed under certain conditions, but whether the facility your municipality uses has those is unclear.
See also "flushable" wipes that must not be flushed down the toilet.
That really should be prosecuted for false advertising. Just because I can physically flush Orbeez down the toilet doesn't mean it's safe to do so.
Home composts aren't usually meeting these, their temperature isn't going high enough for full decomposition and you can have traces of polymers left behind. I throw them in the trash for compostable waste because thankfully my collectivity collects these to generate biogas and my guess is they do end up in much larger/managed composts where they can fully decompose.
https://en.wikipedia.org/wiki/Ingeo
I think there's also "biodegradable" plastic which has cornstarch in it which allows bacteria to degrade it, but that's not the same thing?
It doesn't. The plastics in the ocean don't come from your grocery store. They come from fishing gear and from places without municipal trash service.
Honestly? It's basically greenwashing, it doesn't actually do anything at all. No one ever composts this things, and landfilling or incinerating a bag does not harm the environment.