`mesh_final` isn't really the final mesh but the "current" mesh. Adding the
extra word here isn't helpful. This also helps to reduce the size of the diff
in #119968 where the mesh variables have much smaller scopes.
After recent commits, the .cc file is only used for actual object data
evaluation in the depsgraph, and the header is only used for the old
DerivedMesh data structure that's still being phased out.