This is correct, but in practice, this accountability is so diluted that they're free to do whatever they want as far as public accountability is concerned up to the point what they do is so unpopular that a majority of voters across the union decide that replacing the council is more important than selecting their national parliament.

Then there's the commission, which is even less accountable to the voters.

Not really, chat control comes from the comission, the current news is about the councils struggle to formally reach a position on that proposal.