It might be a bug. I have Mafia 3 (ps4) from PS+ on US and SG PSN.
On US PSN, the new Mafia 3 definitive edition is full price, doesn't show "purchased".
On SG PSN, the new Mafia 3 definitive edition was also full price, didn't show "purchased". Oddly there is a "download to your ps4" button. When I clicked that, it started downloading... but that's the demo that it downloads. (I guess I had downloaded the demo from SG psn before, that's why the "try demo" button turned into download button.) I canceled that, checked again, still full price, not "purchased". Then did some exploring (bought the DLCs, went to check US psn, etc), came back, it now shows "purchased", click on "download to your ps4" button, it started downloading the full game (no longer just the demo).
On both PSNs, the DLCs are free though, purchased them with no issue.
So I am not sure owning the previous vanilla Mafia 3 (ps4) will give you the new Mafia 3 definitive (ps4). I don't have Mafia 2 digitally (platinumed it on ps3 but it was physical disc) so I can't test that.