Mostrami frasi di esempio con "media baron" or "gutter press" .Indicami il maggior numero possibile di espressioni quotidiane.

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Ooh, this is actually hard unless one has been reading around the topic tbh.

Pulled from google, I lack access to a corpus but you might want to find access to a free corpora of English for more specific terms like this:
'He became one of Britain's most powerful media barons.'
'Who really makes the best media baron?'
'If the flow of ideas is dammed by media barons... then an irreversible trend may be set toward a monolithic, totalitarian state.'

Interestlingly, 'gutter press' doesn't even have an OED entry yet. I also couldn't find any sentences in the first few pages of google beyond 'We're the gutter press,' a company.
The definition given by wiktionary is that of tabloid newspapers, which checks out. Traditionally, in Britain, tabloids are opposed to broadsheets - tabloids tend to be more sensationalist, short-form, clickbait-y, broadsheets tend to discuss matters in-depth.

Examples of broadsheets vs tabloids are given below, I've not tried to stay UK-centric. Some of these aren't traditional newspapers, being periodicals, magazines, or online-only content. I personally feel as a native-speaker that trying to keep this to print-only materials would obscure the fact that in practicality, these terms are used to refer to long-form vs. short-form journalistic content more generally (at least for my idiolect - and I think there is a pragmatic argument for their use in this way.)

Tabloids:
Daily express, Daily Mail, Sunday Mail, Sunday Mirror, The Sun, etc.
Broadsheets (nb.: Some of these are more broadsheet-y than others. The Guardian, BBC and Atlantic, fex., are often more tabloidy despite the excellent broadsheet content they often contain.):
The Guardian, BBC, The Atlantic, The Economist, NPR News, PBS Newshour, AP News, The Spectator, The Financial Times, etc