Based on how 343 appear to be using older versions of the halo story for inspiration (CE's original plot was going to involve cortana going rampant, ansconding with halo and trying to conquer the galaxy) I would guess that:
The enemy will be called the covenant. It will just be Cortana's covenant. The prometheans will be folded into the existing sandbox rather than being an alternative. So instead of crawlers, watchers, soldiers and knights replacing covenant enemies, you will see them back up the existing enemies. Imagine jackal phalanxes with watchers to dispose of grenades. Grunt swarms using crawlers like attack dogs. Elites and Soldiers double teaming you. A fight with two hunters and two knights. That way the new additions feel additive.
Halsey will die during the game. They will determine that they can't match Cortana without an AI of equal capabilities, and they have no cloning facilities nearby. So she will agree to be the basis for a new AI to match cortana. Said AI will effectively be a new cortana and be voiced by jen taylor so as not to alienate the fans. It will be a bittersweet moment because we sortof get cortana back...but it isn't OUR cortana. Also she will be named Joyeuse (a reference to Bungie's cortana letters) and Cortana will be PISSED that MC replaced her. the conflict between the two AI will parallel the fight between Mendicant Bias and Offensive Bias in the lore.
GAMEPLAY:
Not open world, but the worlds will be big. Think Dragon age inquisition or Crysis. Mission structure will be similar to the second mission of Halo CE where you can go after the drop pods in any order. The game will give you an objective [go here, shoot this, defend that, steal this] but will leave the specifics up to you.
We see from the boxart that Chief is using the MA37...which is an obsolete covenant war era gun. I think that due to how OP the new Covenant is, the unsc will be forced to use whatever tech they can scavenge. This will give 343 an excuse to mix the new designes people like, like the new BR with classic designs that are outdated in universe like the SPNKR. I also think all the vehicle and gun variants form warzone will appear in game. This is how they will handle exploration and secondary objectives. The base game can be played like a typical Halo game, but if you go off the rails and explore, or do side missions, you can find old caches of covenant, forerunner and UNSC tech which will allow you to unlock more advanced guns. So you start with an outdated rifle, and as you get through the game you can upgrade it with hardlight or shredder rounds, and finally upgrade it to an MA5D. You could even have the legendary or mythic versions of weapons hidden behind tough optional encounters.
Also: they will finally give us a mission where we control a Scarab. You will use it to fight a guardian and it will run like absolute shit on the OG xbox one.
And before you people say i am being crazy I will have you know I predicted Phil spencer getting promoted to head of xbox before the xbox one was even unveiled, and predicted the next xbox would be named Xbox (admittedly it was one of three guesses) and I predicted cross gen compatibility. I've got some weird shining thing going on with xbox.
Thank you for listening to my ted talk.