I'm speaking of unique cards. I know there are over 16,000 cards but many of these are the soul attendants and evolving wilds, cards that do the exact same thing as other cards with a different name. Has anybody seen an estimate on this?
The "functional reprint" question is very tricky. I'm not sure what purpose that's for, and it really depends on how you define functional reprint - whether you use Wizards' policy for the Reprint list or a more broad definition that counts Civic Wayfinder to be equivalent to Borderland Ranger.
Distinct cards (ie. with different names) is 11206.
But if you wanted to collect one of every card every printed, then its notably higher, for instance there have been 12 different printings of Birds of Paradise & 13 of Wrath of God. So if you take that definition, then 16k is probably a touch low.
It also depends on how close you want to call something a functional reprint. There must be half a dozen vanilla 3/3s for 3R in the game, but they all have different creature types, some more relevant than others. Even in your own example, Soul Warden is mandatory life gain while Soul's Attendant is a "may" effect.