But doesn't registration also entail working for SHIELD as a superhuman operative, or was I mistaken about that too? For instance, if someone didn't want to use their powers, could they just register by giving SHIELD their information and be done with it, or would they have to suddenly start using their powers in the government's service?
This must have been addressed at some point in the comics, considering how much of a difference it makes in terms of what the SHRA actually is- the former option makes it basically just a gun license for superhuman powers, while the latter option is tantamount to slavery like Luke Cage said.
Registration entails answering some questions for SHIELD and being trained by The Initiative, operated by SHIELD. Being trained doesn't guarantee a spot on any team. It's just part of the registration process. Butterball is one of the characters from The Initiative who trained and registered, got his card, but wasn't admitted to any team.
There were a handful of superheroes (Firestar) who stopped using their powers, and nothing seemed to happen to them, but it was made clear via Jessica Jones that you can't just opt out of registering.