The candidates for prime minister and similar positions tend to be front and center during an election.
From what I remember the head of the european commission was picked from a group of people that weren't even up for election after the official candidates that were paraded around during an EU wide election where dismissed.
That's not the point. Voters generally can't vote for their preferred EU policies because they come bundled with internal policies which are obviously much more important for voters.
It's a bit like with replacing senators in the US with state governors (except actually worse since US is way more centralized and local and federal parties are much more aligned).
If voters actually voted for council representatives directly they could actually influence it in meaningful ways. Now e.g. in Germany a CDU voter won't suddenly switch to AFD or Greens just because they prefer their stance on Chat Control (or whatever else).
Honestly, this is a criticism I agree with. I really would prefer if the EU councilor for my country was either voted for (or even indirectly picked by the EU parliament members for my country). At least this would ensure some sort of alignment with EU policies I care about.
The fact that the head of state is on EU council sort of sucks, because when I vote on national elections people are looking at internal issues, and EU policy is more of an afterthought.
But that doesn't align with morons claiming that those are "unelected officials" or that the EU is somehow undemocratic.
I am still to see as many people getting riled up about how those countries are not democratic.