In GR, black holes have only three distinguishable properties: mass, charge, and angular momentum. If you have one made from matter, one from antimatter, and one from sufficiently concentrated light, all three are indistinguishable.

As I'm not a physicist, I wouldn't risk phrasing this as "pure gravitational binding energy" just in case this has a specific and different meaning.

I read the interior of an event horizon immediately causes problems with quantum mechanics' no-cloning rule, so I suspect the actual problem here is "QM and GR are fighting again" and we can't get any answer until we've resolved that.