The GDR denazified much more thoroughly, especially in the conservative /monarchical-leaning juridical branch, with well known consequences (eg, lack of judges with proper education).

But on the other hand, didn’t the SED give old Nazis a political home in the National Front, supposedly to keep them in check and prevent them from potentially becoming an opposition force?

GDR was not alone in using this strategy, but I’m not aware of anywhere that didn’t end up lending a lot of legitimacy to fascists and coming back to bite them in the end. Same story played out in my country of origin, but there it was the centre-right that decided that they should absorb the fascists in an attempt to control them, and it predictably backfired.