Not sure what you mean by "embed a Context within a larger struct." It's certainly possible to have a struct field of type context.Context.
If the object you embed the context in has all the properties of a context (short-lived, request-scoped, passed to every function that needs to handle it, and provides a way to create a nested context) then embedding the context is at worst unidiomatic. This is how http.Request did it to preserve backwards-compatibility; http.Handler usage was too pervasive to ever change its signature.