I cheer that you have engaged with the topic!

First a brief note: Josef Hartinger's investigations, while laudable for many reasons, were for murders carried out years before the start of the holocaust. The investigation was carried out at a time where the Nazi control over Germany was still solidifying, and though it would have taken a great deal to shake it, it was suppressed to prevent revealing the treatment of political prisoners which could have destabilized the still shaky Nazi power bloc (Mainly Germans accused of being communists were killed, it seems. I can't find the reason for imprisonment for many of the victims, although I'm sure they are recorded somewhere).

If we want to really break down into the legality of the Ermachtigungesetz we're going to need a big pot of coffee because that's going to take all night. In short though, yes, the holocaust was legal in that it was authorized through the actions of the chancellor. The position that legality is only conferred by explicitly declared laws is one that sounds reasonable, but wasn't supported by the (obviously Nazi-dominated) courts as the regime progressed.

By that extension then, yes, the holocaust was legal. Was the murder of an individual jew legal? That's... much more complicated (strictly speaking no, murder of an arbitrary jew would probably not have been legal - but the legal definitions of what constituted "murder of a jew" were so absurdly warped that there was no chance of that question ever being asked in a court. For example extermination didn't count as murder, so hey. Also, resisting being murdered was justification for murdering a jew in "self defense". Nazis, lovely people.), but the mass extermination was carried out by order of the cabinet, and that those orders were secret does not have bearing on the legality of said orders.

What the Nazi regime did was absolutely in violation of the laws of the Weimar Republic (and those various governments that came before it), but the reich was not the Weimar Republic and it went out of it's way to overwrite and pass laws that explicitly allowed the arbitrary superseding, suspension and nullification of those laws the Nazi cabinet and the Chancellor saw fit to dispose of. The Holocaust, under Nazi rule, was legal. The Holocaust, under the text of the laws Nazi rule used as a basis was not legal. The Nazis had a move-fast-and-break-things approach to governance, and the Nazi legal system was forever in the process of sorting out the legal implications and precedent of whatever new bit of insanity had just been handed to them.

This concept, that the Nazis were somehow doing this completely without legal justification, is often used to isolate the actions of the Nazis from the greater German population. That is wrong, and dangerous to reinforce - it downplays the role the population had in the rise and rule of the Nazis, and tacitly sweeps that support under the great rug of history by implying that the Nazis seized power, rather than being given it by a population that overwhelmingly supported them right up until the end of Nazi rule. (Yes they did brutalize their way to power, but that brutality only happened in a supportive political climate and with huge support from other parties who either aligned themselves politically with them or hoped to co-opt the Nazi's popularity for their own ends (which did not end well for them...))

It inherently presents the Nazis as somehow illegitimate, having hijacked their way into power against the established norms of the country and that they were somehow simply ignoring those established rules. The classic whitewashing of "They were so evil they even broke their own laws!!1!".

This is blatantly not true - the Reich was absolutely a legitimate governing body, recognized by damn near the entire world, even hosting the Olympics, and their executive structure was no less legally legitimate than any other in the world. They were, by the time of the holocaust, a dictatorship. This is how legality in dictatorships works. Internally what they did was completely legal, and even their actions would have been illegal under the prior laws, they very legally superseded those laws.

It's the same sort of bullshit apologia as the "the average German citizen didn't know about the holocaust!" thing - it's just not true, but it's repeated by the modern-day neonazi propagandists so much that people truly believe it.