Nah.

The European Parliament is impeccably democratic, its members selected by direct vote of EU citizens under a Proportional Vote system

The EU Council is way less democractic, being just made up of representatives of each local government in Europe with zero representation for any political forces not in government. It’s like a giant First Pass The Post system with electoral circles the size of countries, only worse so since citizens don’t directly vote for them, they vote for the people who nominate them. Also in practice there is very little oversight over their actions since the Press barelly talks about them.

The EU Commission is even less democratic than the EU Council, since it’s members are nominated by the latter, so it’s even more indirect. It’s supposed by tradition to be one comissioner per country so nowadays there are a lot of commissioners for “irrelevant thing” and the whole thing is the result of a massive game of horse trading and cronyism, especially the head, with the result that plenty of comissioners are complete total crap - the only time my country had somebody as the EU commission head, it was one if not the most crooked Portuguese politician ever to hold an international position (almost the opposite of the current head of the UN who is also a Portuguese) and it looks like Germany is currently suffering from the same problem.

Unsurprisingly, most of the “unbelievably authocratic” shit comes from the Council or the Commission.