This probably differs from country to country though. I have worked and lived in Switzerland (I know, not EU), Germany and US, and it does not feel like people don't care here in EU. In fact, in terms of people going out on the streets and demonstrating, it takes a lot less in countries like Germany and France to so compared to the US, in my experience.

For example in Switzerland, there's the instrument of a "Volksinitiative". If you can collect 100k signatures, the government must hold a national election on this issue. And these are quite common and popular in Switzerland. In Germany, those unfortunately only exist on a state-level, not federal level, but are also common.

So, in my experience, people are very much involved in government here. This might be different in different EU countries of course. Or maybe you have a vastly different bubble you live in than I do.