In the meantime i've found that I am indeed causing the connection error. I think it's because I have an update that needs to be done. However I keep getting errors for this as well, but I'm finally at 50%, so hopefully the update will complete now.
It's a bit odd because when I looked at the specifics it actually looked like my 3DS wants to update to the Welcome Amiibo update, when I have that update installed for suuuuch a long time. I hope it'll all work out