NewPatchDialog/PatchesWidget: Use forward declarations where applicable

PatchEngine: Minor changes

Makes the enum strongly typed. A function for retrieving the string
representation of the enum is also added, which allows hiding the array
that contains all of the strings from view (i.e. we operate on the API,
not the exposed internals). This also allows us to bounds check any
querying for the strings.

Avoids needing to include Core headers in UI-related header files,
preventing unintentional propagation.

Avoids potentially using the values uninitialized. While we're at it,
also drop the prefixed underscores from one of the constructors.

Including <iostream> causes a static constructor to be injected into the
translation unit, even if the everything from the header itself is
unused.