I've heard it claimed that the expression "Shimshon HaGibor" (Samson the Mighty) [as a descriptive of Shimshon in Tanach] was invented by the Zionists, to promote their "strong Jew" narrative. Is this true?
The rumor is false. The earliest I can find the phrase 'Shimshon HaGibur' goes back to 1831, long before modern zionism or Hertzl.
It can be found in the book צמח דוד
Google books also shows other phrases such as Shimshon our Hero from books in 1801, but those are in English and not the exact phrase. I would not be surprised to find it occurring even earlier than that.
Firstly, the צמח דוד, referred to in another answer, was actually first printed in 1592. Secondly, the first source I've found is מכילתא דרבי ישמעאל; the term can also be found in סמ"ג, in ספר חסידים, in Maharsha, and in numerous other seforim.
On the other hand, the incidence of this term is not particularly frequent. If we replace 'Zionism' with 'Modern Hebrew Literature' which is commonly said to have begun in the mid-1700s, it is quite plausible that this might have done much more than the handful of traditional sources to popularize the term. Conversely, the term may always have been more common in the vernacular as opposed to formal, religious writing, and it might have been only the modern Hebrew books which adapted it as a preferred literary appellation.