Q: when editor clicks on a table header column (of child items table) in main content view, to decide sorting of children, is that setting supposed to be remembered or not when navigating to other nodes then back?

a1: this setting should be carried along while browsing across all content, ie all nodes sort the same

a2: this setting should be remembered on a per-node basis

a3: this settings is not remembered at all, when going to a node the default sorting shown is the one decided by the actual node-sorting parameter

I vote for a1 or a3 (a2 being too confusing, as we already have a set-child-sorting button).

But it seems the correct answer is a3 - except that when sorting of children is set to path_string or class_identifier, the children table shows by default sorted by the "published" column