Is there no way they could have framed it that would make it clear that you get support for the thing that you are paying for? Maybe it's because I'm a software developer, but it seems pretty easy to understand that if you're paying for the push notifications API, then you're paying for the push notifications API. Support for the rest of the self-hosted app doesn't come along with.

If you're a software developer, yes. If you want to have this in an org where there are non-technical people, explaining it to them may be a tad more problematic.

Not even dev. Some problem will come along and someone will bitch on twitter, guaranteed.

I work for a company that offers both a cloud and support for self hosted version and if anything offering support is more expensive than the cloud version