The EU isn’t any more neolib than its member states, in fact, often much less so. It raised worker’s rights and living standards pretty much everywhere, it’s actually doing shit against anticompetitive behaviour because Berlaymont isn’t nearly as caught up in national industry entanglements as, well, the national governments.
Is it without fail? No, no government is. But it’s kinda telling that the forces behind Brexit wanted the UK out so that they could continue to park their assets in tax havens, regress on worker’s rights, well, things nobs do.
All in all what you’re seeing from the EU, overall, is European SocDem pan-continental compromise stuff. I can definitely fucking imagine worse, especially considering our history of being at each other’s throat all the time.