Television and radio are advertising media. If the unspecified Federation economic arrangements don't use money, it is unlikely that they use advertising. Previous experience with mass media sold for content rather than advertising is limited to theater, magazines and novels.
That suggests there would be far less content produced. The only regular contributions would be the equivalent of the old time magazines, like Saturday Evening Post or Charles Dickens' magazine, either featuring a miscellany of forms and content producers, or the opposite, a vehicle primarily for a popular favorite plus extras. Except even these equivalents would be less common, since there would be no advertising offsetting production costs.
Basically I suppose that in a sense all productions would be amateur productions, relying upon personal initiative and whatever personal resources are available to individuals. It is true that Voyager's Author, Author! gave the Doctor a publisher, but it is hard to see what such a person did, or why he did it. But since the episode was yet another Voyager episode criticizing studio execs, it wasn't a seriously considered SF projection, not even in Trek universe terms.
Under this theory the "amateur" actor, director, producer can be just as professional as the starship officer. If everybody is in effect working for nothing it means little if one betters himself working a shift in a department on the Enterprise or he betters himself producing the future equivalent of a podcast