So here's what I think is going on in the Campaign:
Like the new Halsey AI explains, she was built to infiltrate the Domain, and commit AI Identity fraud to help drag Cortana out with her. This is probably where the hidden audio clip from the first trailer and possibly that coresponding Cartographer scene are from.
The Operation works, but on the way back to Infinity with Cortana probably to have Halsey do something or for some trial, the Banished attack the UNSC's fleet allong with this "Harbinger" who I'm guessing is Composed Didact. Didact has taken interest in Cortana after she helped defeat him and then took control of basically the entire remnant of the Forerunner Empire.
In the attack He steals her, leading to the new Halsey AI to assume she was deleted.
The UNSC get absolutely bodied in this attack leading to the start of the game that we have seen.
We fight the Banished trying to fuck with the Halo Ring as a targeted doomsday weapon.
Chief beats Echarum and stops the Banished in the Short Term, Atrriox and the faction as a whole will still be at large.
By the end of the game we learn Cortana is alive, Harbinger is the Didact, we may or may nor fight promethians in the base game.
Flood may or may not be in the base game. (Leaning not)
Further story developments left for DLC, where we will eventually see Flood, Promethean and Banished trading off focus as threats.