Federally funded != State Affiliated. There is no one from the Biden Administration telling them what to say. By labeling them as such, Elon/Twitter are implying that NPR has a Goebbels-like figure running it, which is mendacious at best.
Perhaps more relevantly, by expanding the use of labels indicative of state association beyond the original use of “state-affiliated media” for those orgs which are editorially controlled by governments, Musk decreases the impact and clear distinction of that label, further normalizing and empowering the actual editorially-controlled state propaganda outlets operating on Twitter.
NPR was founded by the CPB, which was created with an act of Congress and is governed by a board of directors selected by the President. If it's "mendacious" to claim NPR is state affiliated, presumably it would be completely accurate and correct to state NPR, an entity that was founded and continues to be funded by a federal government body run by presidential appointees is "not state-affiliated"?
Yes that's how words work, NPR is not State Affiliated media. No one from the government is there dictating what they report on or what projects they pursue. When a lab at a private college takes NIH funding to do research, that does not make the private research institution state affiliated. When oil and gas companies accept government subsidies, they are not labeled as state affiliated (and in this case oil and gas are far more deeply intertwined with the levers of government). Elon Musk is a reactionary polemic and these choices are obviously intended to further those goals.
"There is no undisputed definition of state media or government media. The most common definition of state media or government media refers to any media organization that is either directly or indirectly owned or operated by the state.[4]"
"...State or government media can range from media outlets that are completely under state control to editorially independent public service media outlets.[1] The term "public media" can be used to refer to state or government media and public service broadcasting (PBS). Although there are differences between them. According to the ACE Electoral Knowledge Network, state and government media are directly controlled by the state or government; and PBS are not.[7] According to Facebook, state-controlled media are "partially or wholly under the editorial control of a government".[8]"
Interestingly:
"Twitter uses the term "state-affiliated media" and defines it as "outlets where the state exercises control over editorial content through financial resources, direct or indirect political pressures, and/or control over production and distribution." At the same time, "state-financed" editorially independent media are not considered "state-affiliated".[9][10]"
"The goal of the ACE network is to provide knowledge to people working in the field elections, with the intention of supporting credible and transparent electoral processes with emphasis on sustainability, professionalism and trust. "