How could I animate a model that has been created from high-fidelity scans with blend shape-based facial rigs?

Should I find a set of Unity|Unreal plug-ins and packages (middleware, libraries, tools, etc...) that separately do speech synthesis, lip sync, cheek movement, eye rolling, etc...?

I know this is a broad question, but I would appreciate some pointers to help me understand how I can create verbal & non-verbal behaviors in such a model when I open it in Unity|Unreal in order to create a primitive virtual human.

You will definitely want a plugin.  It takes years just to figure out how to do it.  I don't know how to do it.  So yeah, use a plugin.