I would conduct Inititating, Planning and Executing for what I know, as either the first phase of a project, or the first project in a program. An advantage of doing it as separate projects is you will be able to declare victory more frequently. If you do it as multiple phases in the same project, you may not be able to do that. In our organization, for example, we write closeout reports and concut adminstrative closure for projects, but not for project phases.
Which way you do it will depend on details of the situation in which you are involved. If you know enough to plan and execute the first phase (or the first project), then do that. Often, though, in this circumstance, the first phase (or project) feeds the next phase (or project) which feeds the next... and so on.
This may mean you can treat what you are doing as a program (a series of projects which must all be executed to achieve the desired business benefits), in which case it may make sense to dub them separate projects.
"At this stage, we have initiated the project and established a set of requirements, scope, and deliverables to manage the discovery and assessment phase" could be a project with some concise deliverables called "Cloud Platform Requirements".
"... with the goal of ultimately delivering approved future state designs for... " could be a project with some concise deliverables called "Cloud Platform Design".
"...implementation." could be a project with called "Cloud Platform Implementation".
Your organization may decide at the end of a project that you don't want to move forward due to reasons such as a lack of products to meet the requirements and no desire to build anything, or products that meet the requirements but are too expensive, or a change in priorities that can happen when the covers are pulled back and everyone realizes they just want to put it all on pause and spend the time and money on something else.
I would advise against trying to lump it all into one big project, which could lead to planning what you don't know. That could land you in the situation jokingly described by one of the key note speakers at the LA Summit whose father supplied some PM jokes for us:
"Make sure everyone knows the project budget is just a down payment.". ;)
He also said "A no risk project is one that is finished." or something like that, but that is another story.
