Okay I got it.
So like what happened in Episode 4 where new players get to choose to start on episode 4 as a character with amnesia from cryosleep, so that they can skip episodes 1-3, since players who completed episodes 1-3 will basically be waking up from cryosleep too.
They might do something similar for NG where new players who start in NG get a different introduction than plays coming over from PSO2. Maybe players coming over from PSO2 are waking up from a thousand year old cryosleep on the Mothership after some event that has not happened in PSO2 yet cause the story in PSO2 is not over yet. They will likely continue the story in PSO2 for as long as they can to show how universe became the way it is in New Genesis or at least keep it going for as long as they can.
Ancient Arks members are discovered in their cryopods by new members of Arks and they get brought back but do not remember a thing, so they work together with the new Arks and try to figure out what happened and what this new enemy they are dealing with is as they uncover ancient history of their past.
This means we are not really going back and forth. Once our character time skips we will not remember what happened that put us into cryosleep for that long cause it has not happened yet in PSO2. PSO2 will likely continue to the point where some hints of the origins of the Dolls is revealed but afterwards the content will be focused entirely on New Genesis. I think this is a brilliant plan to revive both games, especially if they add in something like; New players starting out from New Genesis can travel to the past and play PSO2 and relive those events through a different perspective or something like that.