EU has done really well on passing big laws such as GDPR in the recent years, while the US can’t even seem to decide whether to fund their own government. Why do you think Europe is doing better than the US? One would think that since EU is more diverse it would be harder to find common ground. And there were examples of that during the Greece debt crisis. But not anymore, it seems.
In terms of the EU what works are laws, which do not require complete consensus of all countries. As soon as somebody can veto, that is nearly guranteed to happen, in many cases for reason with only partial relation to law past. That happend for example with Hungary and sanctions on Russia.
Other then that diversity. There are 7 large groups in the EU parliament for example, but they are then made up of individual canidates from different parties. So basicly no group can push throu laws by themself and the individual canidates often vote against the groups intrest as well. Not most of the time, but it is relativly common. But everybody knows compromise is needed and so they work together in per law alliances to pass laws. A similar thing happens with countries as well for votes which do not require everybody to agree. You basicly just need a few of the big members to agree on something and then form a temporary alliance with other members. That is were this France and Germany run the EU stuff comes from. Both sites politicans meet each other a lot and when they agree on something, it tends to be well enough thought out and a good enough idea to get other smaller members to agree on it, to pass it.
That being said as soon as vetos are involved nothing works anymore, which is why some things have to be moved to non veto as soon as possible. Mainly foreign policy.