No specific rust experience with either, but some thoughts on the popularity reasons outside of the language:
I suspect a bit part of this difference in framework popularity may be due to GTK being more attached to gnome and friends, and by extension, Ubuntu (for better or worse, the most used desktop distro for quite a while) Most of the time that’ll be mainline Ubuntu which has always been GTK.
So if a developer or company is going to target something, then it may come down to “what is the ideal platform to build on for Ubuntu as our main target? GTK? Cool, that’s what we will use.” Of course, either framework is just fine, and either framework targets other OSs as well. I don’t have any experience with either, but it wouldn’t surprise me if the choice of GTK more often is akin to Swift + Apple’s toolkits for iphone development being more popular by a large margin than Ionic/Capacitor, React Native, Xamarin, etc, even though the others provide some benefits (and some significant context-dependent downsides, of course)
If i remember correctly, Qt was not fully FOSS for a while, so GTK was much more widely adopted and recommended early on. But that was pre-2005, I think.