en.wikipedia.org/wiki/Mafia_III

Official 2K materials say the digital version of Mafia: Trilogy was available immediately on May 19, 2020 for PlayStation 4, Xbox One, and PC. 2K's May 19 announcement states that buyers of the trilogy could access Mafia II: Definitive Edition and Mafia III: Definitive Edition immediately on those platforms. A later 2K Newsroom post from August 27, 2020 repeats that players who purchase Mafia: Trilogy digitally can access Mafia II and Mafia III immediately, and would only download Mafia: Definitive Edition when it became available on September 25. So September 25 was tied to the first game's release inside the bundle, not the initial release of the collection itself on PlayStation 4, Windows/PC, and Xbox One.

2K's official May 19, 2020 announcement says Mafia III: Definitive Edition was available that day both as a standalone purchase and within Mafia: Trilogy. The same announcement says buyers of the digital trilogy could access Mafia II: Definitive Edition and Mafia III: Definitive Edition immediately. A later 2K Newsroom post also says digital purchasers of Mafia: Trilogy could access Mafia II and Mafia III immediately, while September 25 was when Mafia: Definitive Edition became downloadable inside the bundle. That means Mafia III: Definitive Edition was not only included "later," nor was the trilogy itself first released in September 2020.