Many years ago I talked to the MNDOT head of passenger rail operations on the phone for something like an hour about all the various plans and challenges of the various corridors. He told me that the "second train" to Chicago wasn't really so much about the second train per se - in a political climate where new rail projects are super difficult, they were using the "second train" project to make speed and reliability improvements on the Minnesota sections of the track, which meant removing many grade crossings, fully signalizing others, straightening curves, rebuilding track, etc. It was tied to the second train project because a non-Empire Builder service would have to be reasonably reliable in terms of schedule to be successful, and all these little improvements could be made without massive environmental reviews and big funding requests - they could be knocked off individually as funding became available. Mind that's my recollection of what he said, many years later, so the details may be slightly off.
But anyway, my guess would be that "environmental and design work" mainly means the design and engineering to finish off those projects, which can more efficiently be done in one contract, even if the individual improvements are meted out over time as funding allows. At some point, with or without any big formal process, the Minnesota portion of the line will have reached a level of quality where time and reliability aren't harmed on Minnesota tracks. At that point, they can start rolling a second train, assuming the Wisconsin section isn't so bad as to prevent the line's feasibility.
Mod note: fixed formatting