Casting foam inlays isn't all that different from creating a silicone mold, except the mold is mostly pressure-sealed; the foam creates a lot of pressure, so the mold needs to be strong enough to handle it.
The foam is related to Gorilla Glue, so it takes meticulous prep and plenty of mold release everywhere if you want to be able to take the mold apart and remove your insert. It has short working time, so everything must be ready to go once you start, and you don't have much time for cleanup. If you've never done a large, complex casting, this would not be a good starting project.
Creating the foam inlay is similar to making a mold of what will be the cavities. If you want complex cavities, you'll need to make complex forms.
Vacuum-forming a positive cavity shell will create an oversized (loose-fitting) form, unless you vacuum-form an undersized pattern. Vacuum-forming the actual items may work if the cavities are deep enough, especially if you cover everything with a foam top sheet inside the briefcase. The foam builds enough pressure to potentially break the mold shell, so a positive vacuum-formed cavity mold will need to be backfilled with something solid, like plaster, to avoid it being crushed.
Alternately, you could use the vacuum-formed shell as a negative to cast a solid replica of the items, then use the replica for the cavities in the inlay.
Here's a good tutorial video showing details of a similar project (making a foam inlay for a drawer for camera equipment): https://www.youtube.com/watch?v=OYP-l4VwKF0.
This kind of application is typically done with foam sheets, though. It's a lot cleaner and easier. Rather than starting with a thick sheet of foam, it's usually done with layers. Here's a video of a guy making a tool drawer insert from foam sheets from a craft store: https://www.youtube.com/watch?v=rbKtUvpUCyc. In this case, he did it with a cutout in a single layer of the desired depth.
There's a product called Kaisen Foam that's designed for this application. It's a number of layers of polyethylene foam tacked together. You cut out the outline and peel away the waste one layer at a time. For irregular parts, the next layer can be removed only where additional depth is needed. It's stiff enough that you can cut it on a bevel. Here are a couple of videos for similar projects: https://www.youtube.com/watch?v=dwe0QEvG1ew, and https://www.youtube.com/watch?v=G4sjbtSw5m8