I'm interested in Reflection Principles but I can't find any references of works around criteria to classify properties well-behaved relatively to reflection, or at least features that properties must have in order to be reflected.

In a passage by Incurvati L., Conceptions of Set and the Foundations of Mathematics (2020) I read:

[...] equating the hierarchy’s absolute infinity with its not being uniquely characterizable by any property of a certain type K. [...] Little has been said, however, by way of a positive characterization of K. Gödel took the Reflection Principle to hold when K is the class of structural properties, but a full-fledged account of the notion of a structural property remains wanting.

where references to Gödel can be find in Wang H., A logical journey (1996) at pages 283-285, but even there the notion of structural property is left obscure.

I ask for any suggestion and reference around this topic (I am currently studying connections between reflection principles and large cardinal axioms on works of Reinhardt, Koellner, Welch among others).