No, the European Commission and the unelected bureaucrats behind it are the true leaders of the EU.
They are the only long lasting institution that can do time arbitrages (wait for the right presidency to push new regulations), they have the means to pressure individual MPs, and they are the ones holding the pen during the negociations between the parliament and the States. The EC is also the master of the legal agenda, the banana republic-style parliament can't decide which laws they vote.
Because the EC has little to no budget to spend, and its only tool is regulation (that doesn't require cost/benefit analysis btw), they...spend their day regulating. They are not constrained by execution either since the States are in charge of applying and dealing the regulations, however how detached from reality they are.
The EC bureaucrats come from a small elite, remote from the reality of the common man. Ursula Von der Leyen is a good example of this. Fun fact, a phd is required to become a EC bureaucrat, so many of them...just buy the services of a post-doc researcher to write it for them. I used to work with a colleague who did it as a side job.
There's democratic deficit in the whole system as this issue wasn't part of most internal election campaigns, effectively circumventing democratic process, due to lack of input from citizens themselves.
EU severely lacks checks and balances if it tries to be something more than trade union.
The EC has no democratic control, their members are not elected, only the commissioners are "approved" by the european parliament. Its actions are also obfuscated and mostly non-public (as we saw in the ChatControl case, for instance), so citizens hardly even know what's happening.
The president is responsible for the secretaries of State actions, and more generally their respective parties.
No one is responsible for the commissioners' actions, and they can't be fired. When Von der Leyen lied and refused to show her text messages where she privately negotiated Covid vaccines, nothing happened. When the EU commissioner for digital markets left and got hired by Uber right after... nothing happened, as no one was responsible.
Commissioners hold the legislative power, as they choose which laws to introduce and hold the pen during negociations. It's pure, unchecked bureaucratic power that ends up with a never ending flow of stupid regulations that weaken Europe slowly.
I'm suggesting that there are enough layers of interdiction, that you can easily 'wash' political fallout and push legislation that would otherwise get you voted out of office in local elections.
Now you can argue there is a democratic deficit in those countries, sure.