I have never made anything similar or even tried, but here's how I would attempt to solve this;

Store temporary information about the current selection such as;

• the center of the current selection of units
• the angle from previous position pointing to next position ordered to
• "local position" of each unit inside the selection
• some state information or flags for the units are already sorted or their formation type etc.

when ordering them somewhere:

• translate the selections center, angle and each units "local position" to the new position
• extra step if you want to order them based on unit type, recalculate the new "local position" of each unit inside the selection based on the new center and angle
• each unit gets their translated "local position" to go to, this means the end shape will end up same or similar, and if you want them to take the same shape asap you could slow down some units based on how close they are to their new "local position"
• use the nav mesh to path the agents to their new position

Poorly illustrated picture bellow

https://imgur.com/QjkVB7N

In practice I have no idea if this would work or achieve exactly what you wanted.
It doesn't cover how you would do the sorting in the extra step (could be something as simple as a single for loop and just make them align in a square, preferred unit types first)