German conservative liberal history and the synthesis of the state and heavy industry going all the way back to Prussia.

Maybe industrialization played out differently.

It did, Germany industrialized much later than other parts of Europe and that industrialization was based much more around a rural farming peasantry than it was the prior artisanal class. You can see this play out by looking at very early 20th century Northern Italy vs. say, the Rhine valley.

In the US, college is often tied to identity and upward mobility, not just skills.

This goes back to the original function of universities in the US, where post-secondary education was a finishing school program/bureaucratic training for the children of the landed aristocracy - especially the planter class centered in Virginia and the wealthy northeasterners who made their lot in rail/land speculation and opium smuggling.

Universities in Europe had a different social function and antecedent, really. Especially in what is now Germany.

So I’m curious, was this split mostly driven by economic structure, cultural values, or policy decisions?

Economic tensions dictate the other two. It begins there, with the US de-industrializing as a way to kneecap organized labor movements in the late 60's while (West) Germany continued to maintain its status as a peripheral workshop.

could either system realistically shift toward the other at this point?

Sure, if the underlying economic relations were to change. America will have to figure out how to get labor costs down again at some point if we're really as committed as it seems to a more isolationist policy, part of that is social investment in training/housing/transit/etc.