The end of the game makes it obvious we are in a new FF7 timeline / universe and the survival of Zach has heavy implications for other characters. Cloud and Co. will 100% be going to Gold Saucer and Jesse will be on stage performing; however, she will have no idea who you are due to her never being an Avalanche member in this timeline.
Hmm, I read it differently. I don't think the party has crossed over into a separate timeline where Zack survived. That would be hella messy. I think that scene was just meant to indicate that there are multiple distinct timelines in play: the timeline we've been following all game (let's call it Prime), and one where Zack survived.
Jessie, Biggs and Wedge all just survived in the Prime timeline we were following all game, as the Whispers failed at several points to preserve the original sequence of events. Zack still died as normal here too, or it wouldn't make any sense for Cloud to be as he is. However, as we see there is an alternate timeline (denoted by the different design of the dog mascot) where Zack survived. Obviously there will either be a convergence at some stage so Zack can meet Prime Cloud, or maybe they will work across the timelines to defeat Sephiroth.
We'll meet back up with the Jessie we already know at the Gold Saucer imo. It would make sense for her to head there what with Seventh Heaven destroyed, several of her friends presumed dead(?) given they disappeared after heading to Shinra HQ, and her own near-death experience.
Typing all of this is still hella gross lol. I hate that they didn't just make a proper remake and we have to deal with all of this timeline BS.