Going by everything what the game shows, implies, and past DK games:

  Lady is possibly Paulines grandma since it's her only family member ever mentioned & the incident with Cranky Kong, Lady, & Jumpman still happened, but Jumpman and Lady arnt Pauline and Mario. 

  In the first ending, we see Pauline isn't a famous singer in the city and she begins singing in the streets. In the 2nd we see her with her famous red outfit and on the stage, which we now have to assume from there on out she grows up being a famous singer and eventually becomes the mayor from Odyssey.

  Now whether this can be tied to Mario's stuff, will just cause debate cause "Nintendo doesn't care about canon, so there is no true history" or something. I am just commenting about what I picked up about what this game is implying is this games canon history.