I'm curious to know if Edo makes it possible to originate/mint NFTs privately, so that no one can see what or how many have been created.
You wouldn't get meaningful privacy. It would be the only asset in its own pool, so you would know every time it changes hands, which might as well be achieved by using fresh keys without any zero-knowledge proofs. The multiasset pool[1] would give you more meaningful privacy, but it's not a part of Edo.
[1] https://research.metastate.dev/multi-asset_shielded_pool/
