What does 'at stake' mean in this sentence

Question

At stake in these trends were a reaction against Romanticism and a reassertion of the primacy of an inherent logic of musical materials.

Two programmes (DeepL and Cambridge's) translated this sentence into Turkish in a meaning like this:

'A reaction against Romanticism and a reassertion of the primacy was the desired outcome in those trends'.

So two different AI translates 'at stake' into Turkish as something like 'what matters is/what desired is/the purpose is ...'

However, at stake has a totally different meaning in dictionaries. From Collins:

If something is at stake, it is being risked and might be lost or damaged if you are not successful.

and it's the same on Cambridge Dictionary as well.

My questions are

1. What does this sentence mean?
2. Do the programmes translate 'at stake' correctly?

To provide a context:

The later 20th-century penchant for historically based performing practices, pre-Classical repertory and period instruments can also be linked to Modernism. At stake in these trends were a reaction against Romanticism and a reassertion of the primacy of an inherent logic of musical materials.

Modernism on Grove Music https://doi.org/10.1093/gmo/9781561592630.article.40625

Answer 1

In this quote "at stake" is not being used literally to mean at risk of being lost or destroyed, but figuratively to refer to a change in the popularity of a certain point of view. It means the thing is an important subject for consideration pending some kind of outcome which could be positive or negative.

Trends and viewpoints can rise and fall in popularity over time, and when a point of view is being challenged, it's "at stake" in the sense that the correctness or reliability of it may be called into question. People who have a vested interest in a specific point of view may see something that brings it into question as putting it at risk in the same way that money could be at risk of being lost.

In this case there's a conflict between Modernism and Romanticism in 20th century music. Reading further you find this... "Scholarly objectivity with respect to history became a Modernist conceit."