If I had to guess how they're going to structure part 3, this would be my guess:
We start with showing Zack or Aerith, just like in Rebirth. Whether this be their reunion or not, who knows. I think it would be best to make us wait a little bit more, since I don't know if players would feel the impact of a Zerith reunion if it was the first thing shown to them after a 3-4 year break. Then, just like in Rebirth with Kalm, we get transported to our party in Icicle Inn. From here on out, things progress as usual, with the added depictions of the party grieving and Cloud further losing himself. I'd also like to guess that Cloud might falter during this time, going unconcious, and having to be carried (by Barret, probably) to the cabin at the foot of Gaia's Cliffs. This could be a nice nod to the OG, and it's also a good time to have another Zack/Aerith interlude.
Then, upon reaching the Northern Crater, Sephiroth will most likely use Aerith's death as gaslighting material along with Cloud's false recollection of the Nibelheim incident. Sephiroth will first show Aerith's death, and Cloud will deny it: "it's just an illusion". He realizes here that Tifa's trust in him is wavering, and he gets worried, but he is still confident it's an illusion. Then Sephiroth busts out the Nibelheim incident gaslighting material, and yet again, Cloud will deny it. This is where we can have Cloud realize Tifa has lost faith in him, just like in the OG, and the confidence that it's all just an illusion fades and his mind breaks.
The reason I say this is because, I think it would be odd if Sephiroth didn't use Aerith's death to some extent to break Cloud's mind. Aerith's death has put Cloud into an incredibly delusional, fragile state of mind, so I feel like it would be really fitting for Sephiroth to take advantage of that.
Everything proceeds as usual, Shinra 'saves' the party from the madness that ensues at the Northern Crater, but has plans to publicly execute them in an attempt to save face. Tifa is out for a week, and I think this would be a good time to have the Zerith reunion, for reasons I will explain later. For now, Tifa wakes up and everything proceeds like in the original, minus the slap fight, I always feel so embarrased watching that scene. Here's hoping it gets replaced with either a swift uppercut to the jaw, or I could even see a bossfight slotted in here, maybe something similar to the fight with Scarlet in Gongaga.
Anyway, this is when the search for Cloud commences, and also when things are escalating between Wutai and Shinra again, since Shinra does fire the canon again to defeat the weapon that attacks them. Like others have mentioned, it would be nice to have Tifa be the party leader for a little longer this time, so I think she should be the leader during the Wutai arc. How exactly the party are going to get wrapped up in it, I couldn't really tell you.
If I had to guess, I'd say this is also a chance to slot in Rocket Town, as the town is very western, and closest to Wutai out of any location in ff7. I feel like it would make sense to visit there to:
1) Ask around for Cloud. Has anyone seen him, places where he could be etc.
2) Justify two visits to Rocket town. Others here have proposed that Rocket Town could be done in one visit, I disagree. Having Cid have his grumpy arc start and be resolved within like 20-40 minutes of gameplay would feel silly and might give me whiplash.
3) Wutai advances are seen, which convinces Yuffie to take action/investigate the situation a bit. She convinces the party to come back to Wutai with her. It would make sense, since they are searching for Cloud at that time, it would be easy to convince the party that he could possibly be there (only god knows where he is at this point in time).
This is also a chance for Yuffie to take advantage of the fact that Cloud, their original leader, is gone, and so she takes the chance to steal their materia and run off to fight in the war. What happens from here to the end of the Wutai arc? Who knows. As others have mentioned, Cloud being gone for this would make us miss him mechanically, so it would be effective in making the player also miss Cloud.
After Yuffie is recruited back to the party, (whether or not the conflict with Wutai is resolved at this point, I can't really say) we yet again begin searching for Cloud. We visit multiple different locations, and somebody, probably Dr. Sheiran, tells us that he has treated many a mako poisoned victim, and that they most frequently come from Mideel, sometimes also washing up there. This could be a hint for our party to visit there, and lo and behold, they discover Cloud, mako poisoned and catatonic. This is where Tifa leaves the party to care for Cloud. As others have mentioned, Dr.Sheiran could follow along, him wanting to get a blood sample from Cloud feels like it's hinting at something.
Then, we catch wind from Cait Sith that Shinra are planning to use the huge materia (either against Wutai, or against Meteor. Probably Meteor). Others have suggested a party split here, but I don't really think that would work. Cloud not being present for two whole huge materia and we are now severely cutting down Cloud's screentime. He's already been gone for a long time at this point, so having him miss even more would feel like a shame, we wouldn't get to see enough of 'real Cloud' as I would like. And also, ft. Condor doesn't really exist as a location anymore, atleast not in the same way it used to, I wonder how they'll slot in a fourth huge materia or if they'll just cut it down to three. Our first stop is Corel, this is also Barret's chance to redeem himself in the eyes of the Corel residents, just like in the OG.
After this, Cait Sith notifies us that a weapon has been spotted around Mideel. The party take the warning and return to Mideel, where a weapon is aggravated and aggressive, and there is a risk that it could attack Mideel. In the end, the weapon does attack Mideel, and the party are there to fight it, and then Cloud and Tifa fall into the Lifestream, same as the OG.
Whether or not those two baby weapons will be involved here, I don't really know. It feels very likely that there are specifically two of them for a reason, and judging by the fact that Tifa's mini-lifestream sequence happened while inside one also makes me think that the two babies will be involved in the same way.
This is also where I think Zack/Aerith will be involved in the LS, and why I think it was important for them to reunite at an earlier point in the story. Last time Tifa went through memories in the LS, Sephiroth attacked her. In the OG, the LS is where Sephiroth really lost, it was then and there that Cloud regained the courage to face Sephiroth again, and therefore defeat him. Sephiroth has been trying his hardest to drive a wedge between Cloud and Tifa for this exact reason, he is going to do everything in his power to prevent Tifa from saving Cloud. This is where Zack/Aerith come into play, since we are in the lifestream already, having Zack and Aerith fight off Sephiroth so Tifa can save Cloud without interruption just makes a ton of sense to me.
What exactly happens during the LS? Who knows, something really worth the build up, hopefully. I doubt we will get a kiss here, it would be much appreciated, and would hammer home that the LS is supposed to be romantic. Maybe we could even get a spoken confession since Cloud's subconcious is more confident in speaking his mind (pardon the pun). But I am doubtful of either of those things happening during the LS.
Post LS, we have Cloud back, and so we start up the huge materia quest again, Rocket Town, underwater facility etc. After that, the party needs to find a way to stop meteor, and so we revisit Cosmo Canyon and the Forgotten Capital, and just like in the OG, Aerith's death is replayed to the party, and this is a chance to give Cloud and co. a chance to see what actually happened, and a proper chance to grieve.
Then we have the return to Midgar, I doubt this part will change that much. Maybe Wutai will be involved, if the conflict with them wasn't resolved earlier, it might be resolved here if so, who knows.
I think UTH will remain relatively faithful. It will start with Cloud telling the party to find what they are fighting for, that he doesn't blame them if they don't return etc. same as usual. I think the scene will have a kiss, it just has to. There has been SO much build up to it. If the UTH doesn't have a kiss atleast, I would be shocked. Whether or not they want to keep the implied sex, who knows, probably not, though.
Then, we return to the Northern Crater, and the final battle will probably be something similar to the one in Rebirth, with the party and Zack/Aerith(/Cloud) fighting Sephiroth across the different worlds.
After writing this, I realize that I forgot to include the purpose of the Clear Materia, but at this point I've already spent ages writing it so, yknow.
Of course, if I forgot anything, please feel free to correct me.