There needs to be common base runtime capable of complex types, objects, runtime redefinition support, exception handling etc.

Languages can vary on top of that.

I agree and that’s what the Lisp machines did brilliantly. In it’s current incarnation, and Turing yadda yadda aside, you wouldn’t be able to do what you can on the Lisp machine if you’re starting with C.

You could do it with a language like Lua on top of C, though.

Exposes an API and lets you use it dynamically but (huge but) doesn't let you modify the entirety of Unreal Engine itself dynamically at runtime.

Its not far from being able to do that, though. UE already has very well integrated, introspective build tooling - whats missing is an editor, basically, that could handle the code-base of UE, and then .. wouldn't take much effort to integrate and complete the dynamic runtime/compiler-onboard loop.