Blender had built-in game engine, but it's been frozen and removed few years ago.
Also Epic is sponsoring Blender Fund too.
https://godotengine.org/article/godot-engine-was-awarded-epi...
https://www.blender.org/press/epic-games-supports-blender-fo...
The only area I could see this in is in high-end movie production, like they did with The Mandelorian for the digital green screen stuff, but the distinction between real-time and non-real-time rendering seems pretty strong.
AFAIK you can't directly author 3D models in Unreal, if anything Unreal has a dependency on tools like Blender.
There is some competitive overlap, but that seems mostly within the realm of real-time vs. offline render for producing video content?
Yeah, Blender and Unreal kinda-sorta do the same thing (3d rendering). But their applications are completely different... and you'd be more likely to see people use both tools together on one project rather than a competition between the tools.