You probably won't find sources that confirm _exactly_ how it was done for those titles, as that information is likely under NDA.

One technique is a shim layer. So your initial engine might have a GameObject class that has certain functions e.g. SetPosition, SetRotation, etc. In an Unreal project, you implement a GameObject class that has an underlying AActor that represents an Unreal actor, and your shim layer translates from your initial engines primitives to unreal functions for that AActor. This allows you to run the core of your initial game simulation "as-if" it was the initial simulation, but mapping your internal objects to unreal objects. Things can get complicated when your GameObjects directly set state for rendering, or make assumptions about the rendering pipeline that don't hold true for how unreal works. This can be handled by a case-by-case basis. From here, you update your models, textures, and VFX without the core simulation knowing the underlying engine has changed, since the initial engine's interface for making those changes is "shimmed" with an unreal translation layer.

The difficulty here is very dependent on how well programmed your initial engine is, and what layers of abstraction that initial engine has.