Sovereignty, noun: the power of a country to control its own government. [Cambridge]
A country, EU member, Euro, Schengen, etc. does not control its foreign trade, has no currency, does not control its monetary policy, does not control its borders (Iceland is a remore island so possibly less of a practical issue and indeed they are in Schengen), does not control its laws. That's the way it is. This includes the people as citizens of that country.
I think you are trying to say that they are still "sovereign" at EU level but obviously that's fallaciously ignoring the whole actual issue of national sovereignty vs. the EU, which isn't just a "change of administrative details", obviously...
Interestingly, with your argument they could equally join the US and as long as they have full voting rights they would still be "sovereign", which I don't think many would agree they would be because the whole point is obviously being sovereign as Iceland and Icelandic, not as citizens of whatever other country.
That's the issue with discussing the EU within Europe at this point, it has become a religion and it is not possible to discuss religion with religious people.