Summary

At the moment "format_private" and "format_private_arg" are only used in  "src/btree/bt_cursor.c" so it makes sense to move them into the cursor implementation rather than keeping them visible at the global scope in session.

Here's the comment from Keith B:

"The reason this is in the session and not a cursor is it's more difficult to add random stuff to cursors (especially the high-level WT_CURSOR cursors, because of the static initialization code), than it is to add a field to WT_SESSION_IMPL, and so that's what I did."

Here's a link to the comment https://github.com/wiredtiger/wiredtiger/pull/7662#discussion_r916359214