Believing you're doing the right thing doesn't give you agency issues, that only occurs if they're too insane to realize what they're doing is wrong.

Yeah exactly.

There is a difference between consciously doing evil deeds but only deluding oneself that is for the greater good as a cheap excuse like Light

And then being so absolutely not right in the head they have no actual clue on what they are actually doing like Arkham!Professor Pyg

There is a difference between being delusional and being amoral.

In the cases of delusional Pure Evil villains, their intentions are not ultimately noble. For example, Light deep down doesn't really want to reduce crime to build a better world, he just wants to become the god of a world that he controls through fear. We can also cite Belos, who deep down does not want to exterminate witches to save humanity but just to be seen as a hero.

Also, there is the fact that delusional Pure Evil villains can have moments where they realize that their actions are evil. In the case of Claude Frollo, there are certain moments where he seems to recognize that he is not the virtuous man he thinks he is, such as when he asks God to have mercy on him during his song "Hellfire".

As for amoral villains, they believe 100% what they do is right, with no ulterior motives behind their actions such as sadism or greed. For example, Douma thinks 100% that he "saves" the souls of the women he eats without any ounce of selfish intention on his part because he is too cracked in the head to realize the seriousness of it. his actions where the delusional Pure Evil villains are just too narcissistic to realize that they are bad people while lying to themselves.