I mean what happens when you press the "Insert" key and the status bar changes from "INS" to "OVR" and the cursor changes to an underscore (apparently this is documented as "overtype" and not "overwrite").
Ahh, ok, overtype is entirely within Scintilla, the only thing Geany does with it is read the status from Scintilla to set the status bar INS/OVR, even the insert key operation is within Scintilla.
So yeah the way to go is a plugin that captured keybindings and tested overtype and if it is on did the new behaviour in its own code, or if overtype is off passed control to Geany to do as normal.