S&box was based on UnrealEngine 4 until late 2020. I think Garry wanted to use the latest and greatest engine, then Valve continued to be friendly with him, and even though Valve wanted Source2 to be a VR platform, it was clear desktop was going to remain relevant, but the content creation tools on SteamVR Environments were a cut-down version of what was actually used to make Half-Life Alyx, but they gave Garry all the tools, and he moved to Source2, and built a .net "framework" to make it faster to develop and iterate in Source2. So Garry's tools are now an open version of the closed tools that Valve didn't want to release that they used to make Alyx.

Finally there's another serious competitor to UE and Unity.

Could assume that.

S&box was initially developed on top of Unreal Engine, but in a backend-agnostic design. It's more like a framework/runtime meant to be portable to any backend engine. Once Source 2 released, S&box was ported to that.

I wouldn't call it an engine because of that. S&box is open source, but you can't run it without a closed-source backend.

Valve isn't keen on releasing Source 2 as widely as Source, and I feel like soon, S&box will be declared the official API interface for the engine, while the backend remains unstable. Kinda like Win32 vs NT.

I'd guess S&box is more an extension of Garry's Mod rather than a reaction to Unity