I have the same suspicion than you that it's the problem. But frankly the pledge account is totally incoherent as there's zero DLC mentioned and zero DLC code.
Moreover I did that ie redeem on gog the copy code because of the crap they did with the Early Access code not supposed to last and then suddenly becoming the final release. So I had lend the second temporary copy and suddenly had lost it as it became the release code.
And anyway it's just f...g flies to not give the DLC with the copy. If it's not solved my Gog account will be a garbage with a part of the game coming from the larian account and a part coming form a box, pff.
Ha well thank you for the advice I'll try that.