If I were to ask what my relatives think of Chat Control I'm certain that an overwhelming majority would not have even heard about it. Hard to oppose something if you don't know about it. But even if they did oppose it - does the average European even know how to figure out how their chosen politician voted on the issue? Probably not.
Maybe it's a lack of journalism, I'm unsure, but I don't see any other reason for it. I also think that this is the factor in euroskepticism.
For reference of discussion in Sweden see https://chatcontrol.se/ (in Swedish). Social democrats and Christian democrats are the ones who seem to be more supportive of this law.
People there have had their freedom since the viking ages and probably earlier, it was never taken from them and therefore never scarred the culture. In other countries where peasants had to fight for their freedom their culture reflects that, but Swedes never had to do that.
So after millennia of governments letting its people be free why start distrusting the government today?
I think that trust in government comes from a mix of things, oppression was probably not a necessity, and centralised control was beneficial to most classes, but I see that there is also a very strong cultural element. Trust in authorities is taught in schools in very early ages, I see this with my children and I can compare to other systems (contrary to most Swedes). The folkhemmet ideology is still very strong in this country, it's almost a matter of national pride. To this add the tendency to conformism (jantelagen) and the avoidance of conflicts at all costs, which makes criticising others very badly seen.
Regardless where it comes from, I find that the uncritic, often blind trust in authorities in Sweden problematic because it hinders plurality and a sane discussion in society, like in the case of the Chatcontrol law. But individualism is also on the rise, very much so in fact, and the society is changing fast, and with it also trust.
I think this is a fundamental difference between the countries that have fought for freedom (like England, France, USA), and the countries where the powers that be saw what happened and made minimal concessions to try to avoid unrest.