We have older fragmentary myths about Zagreus and Hades being related but the ones to him and Zeus were mostly due to the orphic cult fusing H and Z and greeks calling H "Zeus of the Underworld" to avoid his name
With regards to his connection to Dionysus, there's some sources that say Dionysus is basically the reincarnation of Zagreus, in a way. Basically after he was ripped apart by titans/giants, they kept his heart until they implanted it into young Dionysus (or something like that)
The Hades game makes fun of the ambiguity by having Zagreus and Dionysus pull a prank by telling Orpheus that they're linked that way, and Orpheus believed them and told everyone. Thus in the game, the whole reason people say they're the same god is because a prank that got out of hand.
I think Melinoe and Zagreus are Hades' kids
We have older fragmentary myths about Zagreus and Hades being related but the ones to him and Zeus were mostly due to the orphic cult fusing H and Z and greeks calling H "Zeus of the Underworld" to avoid his name
Too much confusion leads to more confusion
With regards to his connection to Dionysus, there's some sources that say Dionysus is basically the reincarnation of Zagreus, in a way. Basically after he was ripped apart by titans/giants, they kept his heart until they implanted it into young Dionysus (or something like that)
The Hades game makes fun of the ambiguity by having Zagreus and Dionysus pull a prank by telling Orpheus that they're linked that way, and Orpheus believed them and told everyone. Thus in the game, the whole reason people say they're the same god is because a prank that got out of hand.