Do I do zero net work if I start and stop a spaceship in vacuum?

Net work on the spaceship is zero, yes. But don't forget all the "thruster dust", as you mention, the exhaust gas. Non-zero net work has definitely been done on that - those particles are at full speed moving away from the spaceship - so the overall net work of this entire system is non-zero.

It therefore just depends on what you are looking at; what you define as your system.

Furthermore, even though the net work done on the spaceship is zero, that does not mean that no energy was lost, of course. The thruster was pointing backwards in order to accelerate the ship, and pointing forwards in order to slow down the ship. Although this causes different signs of work to be done on the ship, a non-zero amount of chemical energy in the form of fuel is released in both cases. That energy is now converted into the kinetic energy of the exhaust gas particles as well as into heat, undoubtedly.