To reproduce from emacs -Q, evaluate in the scratch buffer:

(display-buffer-in-side-window
  (get-scratch-buffer-create)
  '((side . left)))
(split-window (frame-root-window) nil 'below)
(window-main-window)

Observe that (window-main-window) returns the selected window. However, the
window that was created by splitting below is not a side window, and it does not
descend from the selected window. This contradicts part of the docstring of
window-main-window:

"If FRAME has no side windows, return FRAME's root window. Otherwise, return
either an internal non-side window such that all other non-side windows on FRAME
descend from it, or the single live non-side window of FRAME."

Splitting a frame's root window in the presence of side windows seems to often
lead to such discrepancies. I have observed such behaviour in the packages hydra
(on ELPA, in its lv-window function), and shell-pop (from another package
archive).

Related to that: Is the following supposed to be an invariant for each frame,
and should it be considered a bug when packages violate it?

Invariant:
There exists a window MAIN such that for all live windows WIN (other than MAIN)
we have: WIN descends from MAIN if and only if it is not a side window.

This is something I assumed and was surprised to see violated.

Best,
Ferdinand