Fresh pasta is a different category - it cooks so fast. Stuffed is also different.
In your example, the soaking idea would apply as follows:
- soak (dried) pasta before you start prepping vegetables
- assemble sauce as usual in sauté pan
- when sauce is ready, add soaked (drained) pasta with a splash of water and cook till your preference
The pasta finishes cooking in the time everything heats up together i.e. no need to boil first (pasta has absorbed the water it needs already, it just needs heat to cook it).