The Number One Player in the American Comic Universe

My name is Jeno, Lee Jeno, an unemployed dog, twenty-five years old, and I just received a special advance version of the game called "The Only Player in the American Comic Universe". I found that this game allowed me to go on adventure after adventure in various comic book universes. ... BATMAN: Geno Lee is extremely uncertain and loves to use my identity to put the Bat-brand on the butts of Gotham's lunatics. Superman: Geno Lee is a good man, but he always wants to make some strange changes to my uniform, such as replacing my red cape with a rainbow flag, saying that this is the right thing for America. Iron Man: I don't know how to describe it. He is always omnipotent, but always secretly encourages me to develop an artificial intelligence companion girlfriend.... Cap: I have to pray to God to let Geno Lee leave my world, and he changed my shield to the color of Death Barbie pink! PS: Non-fusion world view, the protagonist travels through the universe alone, the current script is "The Flash 2023"