The way this question is framed is way too broad to even attempt an answer so I'm just going to point out a distinction.

Almost all countries have some form of legislature or general representative body (e.g. A Parliament). Even China and Iran have assemblies. Iran's is even elected. That doesn't mean that they had liberal revolutions or that liberalism hold any particular sway in those countries or regions. At the same time some of the earliest and best practitioners of democracy never officially abolitioned monarchical practices (e.g. The UK and the Netherlands). So some of the most 'liberal' countries aren't republics (they're monarchies).

It also wasn't an easy path from the ideas spreading to full blown constitutional republics practicing liberal democracy. For instance in the earlier 1800s Germany had the 'march revolution' where it briefly established a nationwide republic. But this was quashed within the same year to be replaced by the patchwork of statelets and later the German Empire. Germany wouldn't see full democracy again until Weimar in 1920. And even then those institutions would be removed when Hitler came to power in which case Germany wouldn't return to liberal democracy until 1949.

The core message of this is that the road from ideas to dominance in practice isn't a linear one. The history of ideas is complex and varied and happened in each nation differently.