The split window is best treated as a read-only view, its does not provide full editing capability. Geany is designed knowing about only one edit window, a plugin may add another editing window, but cannot change the design of Geany. So operations that are part of the editing widget work, since it _is_ the extra window, those operations that are part of Geany do not work since Geany is not written to handle extra edit windows.
There have been several attempts to fix this over the years, but they were either very large changes, or had poor performance (@b4n has GTK3 speed improved for your window switch hack yet?) or were otherwise unacceptable.