Everything is fluid and will depend on the product, company, and process needed, but those are the basic steps.
The incomplete part of the story is once you get to your last step “ME works with EE…” that isn’t where the development ends. If the answer is “no there isn’t enough room” the cycle starts again. Sometimes it goes cyclical, sometimes it’s back and forth, sometimes it’s just a “Throw it over the wall” and never touch it again model.
If your area of concern is CAD - then that’s again a huge varying between companies. In an ideal world, the engineer and designer work in the same package. Pro E, Solidworks, Catia, etc so that the ID model and Final product are as closely related as possible. There are also workflows where you can hand surface data (Alias/Rhino) to a parametric CAD package (this is common in the auto industry where surfacing standards are the highest). In that case the import/export procedures will depend on the software used.
Then sometimes the designer will just build a model in whatever and the engineers will rebuild the design in their tool themselves. This way they own all the production geometry and don’t have to go back and ask for updated surfaces.
There really is no “best” workflow. Everything will depend on what you are designing and what your budget is. Solidworks is great, but can struggle with massive product assemblies. Pro E can handle massive assemblies, but is not intuitive for Class A surfacing. Alias is great at surfacing, but useless for solid modelling. I guess you get my point.