Similar to this question except I want this as ideally a per-document setting or mode line. The ideal would be something like:
#+STARTUP: showlevels 3
Or if needed as a mode line:
# -*- org-showlevels: 3 -*-
And be equivalent to running C-3 S-tab
when loading the file.
This does not appear to be directly supported in the initial visibility settings in the org-mode manual: https://orgmode.org/manual/Initial-visibility.html