Isn't "homicídio" more like a broad term which includes unintentional deaths (which we'd call as "homicídio culposo")?

Both of the terms "murder" and "assassination" imply intention, with the intention behind an "assassination" being a political/ideological one rather than the intention behind a "murder" (which would be more personally-oriented intentional homicide).

My question is because I can't remember of a Portuguese term that carries a political/ideological sense when referring someone killing another. Portuguese-speaking media outlets here in Brazil often use "morte" e "assassinato" interchangeably, even though "morte" is an even-broader term referring to "death".

Perhaps the Brazilian media lacks an equivalent word, too. "Globo" (one of the major media outlets here), for example, is using the term "assassinato":

Even UOL, another major media outlet which is said to be more left-leaning, is also using the term "assassinato":

So, as the OP said, these headlines, especially in Portuguese, "makes it sound unwarranted".