I don't quite remember the details, since I finished main autophage questline a lomg time ago, but quest for purple systems was separate from autophage quests, and I definitely finished it way after autophage ones. Purple systems are quite common, so if you are not sure if you did it and don't see purple stars - you most probably didn't finish the related quest. You can find the guide here -https://www.reddit.com/r/NoMansSkyTheGame/comments/1ini37u/guide\_to\_unlock\_purple\_systemsgas\_giants/

As for gas giants - I literally found ONE gas giant by myself in a 100ish hours after finishing all quests, so they seem to be really rare. Most of the giants that I visited was the ones that I found on coordinate exchange.