The EU definitely needs it's 'branding' just as does Nike.
You did not even know who Ursula Von Der Leyen was when you went to the polls - she was 'decided' as your leader in a back room, closed door meeting in which MEPs had no influence. When you cast your vote, you had no clue what her platform was, or what she would bring about as leader.
To suggest that this is somehow 'democratic' is a farce. The EU was designed to keep the plebes at bay.
Whether it's the fact that voters have almost no role in leadership selection, that leaders can be chosen arbitrarily, that there is no required vetting process, that MEPs cannot introduce legislation, have very limited power to censure leaders, there is almost zero voter awareness of the political apparatus, the individuals or contemporary issues, low voter turnout, that constitutional rights were ceded to the EU without referendum, or worse, that clear and unambiguous referendum results directed leaders to not cede power to the EU - they did it anyhow. The EU has barely any claim to democratic legitimacy, people promulgating it as such are propagandizing.
Literally French voters unambiguously rejected the Treaty of Lisbon - and it was ratified anyhow ceding major elements of sovereignty.
If they wanted democracy the commission would have direct elections and/or the MEPs would chose directly, and, there would be a lot of rules around campaigning etc. You wouldn't possibly be able to vote for the President of a Commission without knowing who they were. MEPs would certainly be allowed to introduced legislation and censure leaders.
So yes, it does take a lot of 'marketing' to convince people of the legitimacy of something when it doesn't have that legitimacy in many ways.
The EU had nothing to with keeping the peace in the Post WW2 order, that was 1) The Marshall Plan and the American Nuclear Umbrella 2) NATO and existential threat from the USSR and 3) The EEC.
The reason the EU wants their flag in the town council chambers is the same as Nike might want that, or the French Government might want their flag especially in parts of France that are not historically very French i.e. it's a form of marketing/propaganda, like anything else.
I don't like Amazon, so I don't buy from them. If people did that, they wouldn't have their weird company towns and creepy 'high school sponsorships'.