I'm no music historian, so forgive me if any of this is way off base, and totally mis-characterizes the influences at play, but this is my sense:
I feel like the next "sound" is a combination of mainstream pop music, as well as an increase in genre music in general.
Musical theatre has always had an ebb-and-flow relationship with popular music styles, and I feel like we're back in a resurgence period right now.
Whereas, by contrast, I think the defining sound of the late 90s-late 2000s was a more distinctly "contemporary musical theatre" style (think Jason Robert Brown, Ahrens & Flaherty, William Finn, Andrew Lippa, etc.). I'm sure these composers had influences from outside genres, but they didn't feel as prevalent. Likewise, there were plenty of genre scores during that time period, but I don't think they were "in" as much. I guess this was the crop of composers that were most influenced by Sondheim? I don't know.
But over the past 10-15 years, I feel like we've seeing popular music styles come back in full swing.
Right now, I think the "hip," "experimental" musical theatre scene features a lot of folk, indie-pop, etc. That scene is where they're REALLY pushing the medium forward, but they've mostly stayed in the non-profit realm. Maybe shows like Hadestown will help them crossover, but I feel like more mainstream pop sounds are more likely to be the commercially fruitful path.
And I don't mean that in a bad way - I actually think the incorporation of mainstream pop into musical theatre can be very artfully, in ways that also push the form forward. And of course, it can also be very entertaining, and even emotionally stirring.