> Passing a budget is like one of the basic requirements of governing. If the current government cannot accomplish that, it should immediately dissolve and elections be held.
It's important to note that this is a basic principle, almost the basic principle, of English-style parliamentary democracy. You have a monarch who makes decisions (through their chosen government, ever since the English cut off a few heads), and the rest of the Parliament (a bunch of nobles, clergy, and eventually representatives of commoners) is there to withdraw financing from that government when they disapprove.
> We could also have a "cooling off" period after a piece of legislation (like chat control) fails.
We usually do, it is called a "session." The problem is the inability to pass negative legislation (which also has a pretty long history) i.e. we will not do a thing. Deliberative assemblies explicitly frown on negative legislation, and instead say that purpose is served simply by not doing the thing.
The problem is that individual rights are provided by negative legislation against the government: think the US Bill of Rights. Instead, we have systems where exclusively positive legislation is passed by majorities, and repealing that legislation takes supermajorities. The only pragmatic way to create new rights becomes to challenge legislation in courts, and get a decision by opinionated, appointed judges that X piece of legislation is superseded by Y piece of legislation for unconvincing reason Z, and this new "right" is about as stable as the current lineup of the sitting justices.
What we need is to pretend like "democracy" is a meaningful word rather than an empty chant, or more often simply a euphemism for the US, Anglosphere, Western and Central Europe, and whoever they currently approve of. Democracy is rule by the ruled, and the exact processes by which the decisions are made define the degree of democracy. Somehow, elites have decided that process is the least important part of democracy, and the most important part is that elites get their preferred outcomes. Anything else is "populism."*
Decisionmaking processes in "democracies" need to be examined, justified, and codified. The EU needs either to cede a lot more leverage to its individual members (and make that stupid currency a European bancor, rather than a German weapon) OR become more directly responsive to European individuals. If you're not serving the individual states, and you're not serving the individual citizens, you're exclusively serving elites.
* A term made into meaningless invective by elites who hated https://en.wikipedia.org/wiki/Populist_Party_(United_States), a party who believed in things that were good.