Clean up `Operation`

[Phantomical]

The implementation of Operation is currently quite a mess. I'd like to instead clean up the internals so that it makes more sense. The main points of this issue are:

• Move Operation to it's own header so that we can de-clutter Operation.h (Move Operation to a separate header #582)
• Add an alternative data representation to Operation that doesn't use a variant. (Introduce alternative data representation for operation data #585)
• Convert all public APIs to use the new internal data representation.
• Remove the old data representation.

This should mean that it's easier to make changes that involve Operation in the future.