What, did you think right and left were arbitrary? The words are arbitrary, but the meanings are not. They correlate quite strongly with the material interests of the up and down.
Unless you literally belive everyone in the EU belive the exact same thing and there's zero disagreements what do ever.
How individual country influence the EU is there is an invisible battle on putting their people anywhere under the commissioners. There are a lot of career people you will never hear about yielding immense power there and from what I know they do not have a political affiliation how we understand it (left, right, etc.)
If you are a corporation or foreign actor and you need something from the EU you cannot care less about the people elected in the fake parliament. If your chance of influencing or blocking something is in the parliament, you already lost.
Most people have a hard time wrapping their head around this because we actually have a better understanding how the US political system works, individual EU countries or even the CCP.