Is trash talking in sports, boxing in question real or is it something that both fighters agree on to "advertise" or get audiences interested in the fight?

All of the above. The mental game, especially in martial arts, is a big part of the match. Also it creates buzz and is effective marketing.

For boxing specifically, it is absolutely part of the fighters' marketing strategies.

For sports in general, trash talking during a game is "real." Extended beefs that get major media coverage might be intentionally played up for publicity.

The latter but fighters can have bad blood between them too, making it much more organic (Khabib vs. Connor, for instance).