For example, a 600 V DC/DC converter is powered only from its HV input, yet it somehow can run its internal electronics (I guess 3.3 V or something like that). Do they use a small DC/DC converter for this? How would that small converter work?
Once common method uses a depletion mode (normally "on") FET connected to the high voltage to start the controller, then an auxiliary winding on the main transformer (for isolated topologies) starts up a "housekeeping" supply and shuts off the FET to keep power dissipation down. Then the control circuitry runs from the low voltage housekeeping supply.
Alternately a large value resistor and zener can provide a trickle current to start the controller, which then runs off of the aux winding after it's up and running. Not as power efficient as the depletion FET though.