Would using cheat codes be allowed in Any% NG+? I assume at least the All Upgrades cheat would be, but what about Invincibility/4x Damage?

Any% NG+ should not have any cheats except for the All Upgrades cheat. Unlocking just that cheat saves the time/hassle from having to play on a new file & max out all the upgrades.

A run that uses all cheats should be a separate category: call it Cheat%.

Another possible category could be Cheat% w/o All Upgrades cheat