You should look into their origin story if you want an answer. And no, Govt-Funded is also not fair absent an indication of editorial control. The BBC in the UK, the NOS in NL, NPR in the United States, and so on are all official channels but they also have their own editorial staff and only in very rare cases does the government directly intervene in the production (and usually simultaneously on other channels as well). So this is simply Elon playing stupid games, which he seems to be very good at.
NPR was created after the signing of the Public Broadcasting Act of 1967 aiming to increase public education through media, which doesn't really answer my question.
> Govt-Funded is also not fair absent an indication of editorial control
They get this source of funding because that is how they were created and entities that were created through a different mechanism (for instance: to become the mouthpiece for a political stream or for commercial reasons) are a different kind of animal.
The government allocates funds to many things that it may consider useful, such as health care, infrastructure and education. This does not necessarily imply that the government does this to create a mechanism of influence, as opposed to their counterparts in countries that are run as dictatorships. Naming the NPR in the same breath as the Chinese, Russian, Iranian and North Korean state media is mistaken at best and maliciously dishonest at worst. Knowing what I know about Musk it is a fair bet we're looking at the latter.
It should be under the same label as BBC, just govt-funded. Up to you what you think of that. State-affiliated means definite editorial control. Syria etc call those outlets education too.