Well there is NPR but it is quite critical of the government and doesn't have any control over private media
State funded media are news orgs that 100% run themselves, but are funded by the government. This is great for achieving good journalism because they're not incentivised to write clickbait or take advantage of outrage and bias generating sales to people that agree with the bias.
State run media is a terrible idea, for obvious reasons.
Plenty of well functioning democracies have the former, and it's important to identify if there's ever an attempt by the government to turn it in to the latter.
EDIT: apparently NPR is not majority funded by the government now, but was in the past: https://en.wikipedia.org/wiki/NPR#Funding
EDIT 2: PBS is probably the better example.
If a new government did start meddling with the state funded media word would get out pretty quickly because all the people it's staffed with are used to not being meddled with and someone would blow the whistle.
Or phrased in another way: state funded, but not state controlled media is a symptom of quality governance as much as it is a reinforcing factor of quality governance.