The only currently maintained generally available engines used by major studios are Unreal and Unity. Maybe you could count CryEngine, but afaik only one major developer besides Crytek themselves use it. Some indies use Godot, but that's hardly "major studios".
Also, no, the Rust tools are not there. Unreal and Unity both have entire ecosystems around them that are at least as important as the engines themselves. Plus asset stores, support staff, console support, and all manner of other stuff you want when your headcount enters the triple digits. You can download an open source fork of CryEngine (O3DE - complicated story) right now. It's free, and no one uses it, because it lacks the non-code extras.
781 games written with Godot were released on Steam last year. That's 4% of the 18,887 total games released.
The percentage is growing year on year.
As unencumbered engines become more capable, the reason to use commercial engines that extract profit decreases.
AAA studios won't use Godot yet. But eventually it'll be good enough. There are now dozens of open source implementations of some of Unreal's most advanced features, such as Nanite.
Everyone uses Blender now instead of Maya. The same thing will happen with game engines.
Because it has marginal to no benefit over existing c++ stacks, and more important would be economically detrimental because the majority of game developers doing engine coding are c++ developers.
The tools are there, sure, but are major studios using them?