… he isn’t himself a war criminal any more than Sam Mostyn could be considered a war criminal if Australia were committing an ongoing genocide.

Herzog isn’t subject to an arrest warrant by the ICC (Netanyahu and Gallant are), but it’s at least arguable he’s a criminal under international law for incitement to genocide. Remarks by him form part of the evidence in the ICJ case: www.icj-cij.org/node/203447

I think even in the absence of such remarks you could make the argument it’s Herzog’s responsibility (or Mostyn’s, hypothetically) under international law to use the powers available to him to remove the government to prevent genocide.

But yeah, as you say, the statement “the UN has declared him a War Criminal” is factually incorrect in that there’s been no finding or warrant against him as an individual.