>Is Openness then really a feature of personality? Or maybe rather a description of the social behaviour of one person in a specific context?
This is a great question! And it touches on what's call the "person-situation" debate, first popularized by Walter Michel[1]. Essentially there was a major debate about whether traits were a thing or we should just be focused on context-specific behavior. Mischel believed that traits weren't useful, and situations ruled.
In many ways this debate has been resolved by the "person as a density distribution" [2]. People do vary a lot within, and that variation is vitally important. However, their average or "set point" upon which they vary is also important and predictive.
When we talk about the correlation between a trait and some external marker, we are only looking at correlations with averages or set-points, which as you mention is only a limited picture of that person, but it is still useful and valuable to look at. For example, I'm a fairly open person. This means that on average I'm more open in more situations. And this is predictive. It's also important to note that this only loosely predicts what I'll do in any particular situation or at any particular timepoint.
[1] https://en.wikipedia.org/wiki/Person%E2%80%93situation_debat...
[2] https://personality-project.org/revelle/syllabi/classreading...