Am I the only one not seeing The World Between Worlds as time travel? i also remember Filoni saying it's not time travel. At least not in how we usually picture this concept.
For me, The World Between world is just that, a place isolated from the regular plane of existence, a place where the Force converge. Not unlike Mortis. Actually, very much like Mortis. Not like there's a lack of hints hinting about this.
I very doubt Ahsoka could travel through time if she wanted. At best she was just transported into that other place, much like what happened back then on Mortis, and I'm pretty sure the only portal she could go back to was the one she went through. She most certainly could not go into Ezra's time. As such, can this really be called time travel? It's also very likely things are kind of predetermined. Even if Ezra pulled Kanan, he could only go back to his portal, and die anyway. Even if Ezra didn't pull out Ahsoka, she would still survive and would've escaped the battle with Vader, which would be interrupted by the temple collapsing anyway. Which is the aftermath of what we saw in Twilight of the Apprentice.
tl;dr: to me, The World Between World is pretty much useless when it comes to traveling through time, as I think it won't allow events to play out differently. Now, why would Palpatine be interested in that, then? Well, he'd get a pretty useful tool that would allow him to have eyes everywhere, anytime. For someone in his position as Emperor, it's the ultimate tool.