From what I learnt back when the whitelist hack was a thing and we were fumbling around with circumventing copying privileges of allowing non-whitelisted PS1/PSP games to be copied to the Vita, is that it does in fact need to authenticate with Sony's servers before it allows you to copy things between the platforms (to make sure you aren't transferring any non-whitelisted games to your Vita)
So my guess is just that 2FA does something to break that step (might be as simple as passwords not matching due to Vita/PS3 having own device passwords, might be more complicated than that).
Either way turning off 2FA did the trick for me as well, pity however that it broke that but I doubt we'll be seeing an update fix this if it can't be fixed within Sony's own authentication system on their servers.