Correction.
Treat 022-2613 as 022-5432. This is the eShop trick case with no NNID linked.
You can fix it by opening the eShop on Nintendo servers and then try again to link your PNID on Pretendo servers.
022-2613 can happen with correct credentials only if your NNID is not on your console (which is another reason why we never recommend people deleting their existing NNIDs, it won’t fix these bugs). In a nutshell, you are just trying to login with a NNID on Pretendo servers instead of a PNID.