I'm not sure that there's a big enough anti-EU movement at the moment, and where a small group springs up there are plenty of people willing to knock them on the head. Most people, at least where I'm at in the EU core, still think that the energy and inflation crises are Putin's fault. Maybe our government isn't doing the best, but they've been dealt a shitty hand and they're doing their best. Even the member states which were previously closest to openly consider leaving (in my view Hungary and Poland) seem to be playing along with current EU policy. People who simply protest against rising energy costs and shortages are being treated by media as Russian agents and genocide deniers.
It's true that the EU is anti-communist, neoliberal, and undemocratic by design. It must be dismantled just like any other reactionary institution. I just don't see it happening all that quickly, but maybe this winter will set things in motion.