To back up your third point, here is a study of the political bias in the German public service broadcasters (in German):
https://web.archive.org/web/20240207032743/https://polkom.if...
https://web.archive.org/web/20240207032743/https://polkom.if...
But in practical terms, while there are some very obvious gaps and biases, I think the German media system is still pretty good in a lot of ways and everybody does have a lot of freedom.
I'd even go so far as to say - the typical accusations of censorship are mostly from right-wing actors who are not censored, but who demand more views and make a spectacle out of claiming to be censored.