Interaction with the old generic industry seems to be fairly limited. Afaik they use a processed version of oil/ore/forestry/farm resources. I'm not sure if they'll take the new processed resources like plastic or glass. However the buildings at the end of the production line make goods (like cars or toys) that are sold by commercial just like generic industry does.
They interact more with the older specialisations though. The old extractors extract the same raw material as the new ones (timber is timber, ore is ore and so on). It will go into both the old zoned processors and the new processors. I believe the old zoned processors just produce something that generic industry uses and not something that would go into a factory like the car factory and satisfy its needs for say metal, but honestly I'm not sure about this. We don't see what the old zoned specialisations produce other than it's tagged with their specialisation. I'm not sure if they've updated it to be a random version of the new ones or if it's still some hidden intermediate resource.
And yes, resources still deplete. Afaik there's been no changes to that, but there's new maps with more resources than usual and there's the built in mod to make them unlimited.