In the UK for example, the people elect members of parliament as their representatives, but MPs choose their party leaders, and the governing party leadership chooses its ministers without any public consultation or debate. What's the difference?
Voters typically cannot directly stop somebody being named leader of their party or given a specific role within government for multiple terms. If you dislike them, you pressure your elected representative to change that.
Almost all representative democracy is accountability through a representative, not directly through control of government internals & positions.
In the EU we find about it after we vote, after they discuss in secrecy.
In a democracy the government as well are supposed to be accountable by the rule of law. As they are not it is a failed democracy.
But representative democracy still is democracy.
Arcane electoral rules make for weak representatives who gather power by making back room deals.
The real (but not constitutional) power lies in the commission that is appointed, not elected, and has been vacuuming power to itself in increasing amounts.
But, once one or two states decided to elect their senator, it was game over. The other states gave up, and now all the senators are elected.
It's true that both the commission and (perhaps even more powerful) the council of ministers are not democratic. But this is in the hands of each individual country to change. And it's national level politicians who are currently the obstacle. All find it easier to blame the EU than to take responsibility for change. But if one country takes action to increase , even a small one, the public in the others will realise they all can.
We get to vote for our country representatives, who then vote for the MEPs. I don't think there is any EU-wide rule that prevents the MEP nomination process from being open - that'd be country-specific legislation.
There is no rule preventing it from being open, there is also no rule forcing it to being open.
I'm an EU citizen. I have minimal saying in who our commissioner is and what members of the cabinet get chosen.
I have a vote which I give to whatever party. After that, the vote for commissioner is secret; I have no idea who voted for what. After that, the negociations for the cabinet are secret; I have no idea what the criteria are and what the plans are.
I'm not putting us in the bucket of non-democracy just yet but I don't feel it's that far.