Is Hungary a signatory of the ICC?
Yes, and no. And no, Hungary had no legal duty to arrest Netanyahu, and has no duty to arrest Putin. (And why it doesn't even matter if Hungary had/has.)

So the situation is, that the Hungarian government signed the ICC documents, but it was never approved by the Parliament.

And as a parliamentary democracy, the government can not simply declare Hungary to be a member. The parliament needs to approve it. Which it did not do.

From the article below:
“We signed an international treaty, but we never took all the steps that would otherwise have made it enforceable in Hungary,” Orbán said, referring to the fact that Hungary’s parliament never promulgated the court’s statute into Hungarian law.

In other words, yes, the Hungarian government signed it, and decreed Hungary a member. That's why everyone else think Hungary is a member.
But they had no right to do it by decree, the proper procedure was never completed, and that means that (by Hungarian law) Hungary is not, and was not part of the ICC, ever.

Now, because the ICC does not consult Hungary, and Hungarians culturally hate nothing more then others telling us what to do, even if Hungary was part of the ICC, properly, public sentiment would be supporting the position of "we didn't agree to this, so let the foreigners try to enforce it, if they dare to!" even then.

It is not a coincidence, that Hungary crashed the Austrian Empire, tore up the Iron Curtain, and now, crushing the EU: One does not simply tell the Hungarians what to do.

https://apnews.com/article/hungary-orban-icc-membership-60b7658c3a8812926c3c528d941f6269