Auto stop/start requires some (mostly minor) modifications to the engine, as well as updated software so that it is used only in “ideal” conditions. And the engine shutdown is done in a way that makes it quick and easy to restart.
I’m not sure, is it even possible to use these systems on diesel motors?
Of course - I've had a diesel Nissan Qashqai with a start stop system all the way back in 2013. Never had any issues with it.
This is an amusing place where most of the advancement was probably in the starter. The same thing that lets you have a small charger for your laptop has helped get a smaller starter that won't drain after a few starts. There is a lot of work that goes into starting an engine.