Actually, since the street prophet mentions the "mark of the beast" in the opening for Doom Eternal, that means that it takes place in the same universe, because y'know, the Doom Slayer would've become a hero after the Ultimate Doom, Doom II: Hell on Earth, No Rest For The Living, Final Doom, and Doom 64. Since to everyone on Earth it had seemed that he just mysteriously disappeared after Doom 64, religious people probably thought that he might return one day, and when the demons invaded, the street prophet was obviously trying to give the people hope that the Doom Slayer would return now and slay the demons. So yeah, same Earth.