Simple script that makes a button to sync multiview setting across scenes in Blender

sync_views.py

import bpy

def SyncViews():
    for view in bpy.context.scene.render.views:
        if (view.name == 'left'):
            use_left = view.use
            camera_left = view.camera
        if (view.name == 'right'):
            use_right = view.use
            camera_right = view.camera
    
    for scene in bpy.data.scenes:
        if scene != current_scene:
            for view in scene.render.views:
                if (view.name == 'left'):
                    view.use = use_left
                    view.camera = camera_left
                if (view.name == 'right'):
                    view.use = use_right                
                    view.camera = camera_right
            
class SyncViewsPanel(bpy.types.Panel):
    bl_label = "Sync Views"
    bl_idname = "VIEWS_PT_sync_views"
    bl_space_type = 'PROPERTIES'
    bl_region_type = 'WINDOW'
    bl_context = "render_view"
    
    def draw(self, context):
        layout = self.layout
        row = layout.row(align=True)
        row.operator("sync_views.sync",
        text="Sync", icon='FILE_REFRESH')


class SyncViewsOperator(bpy.types.Operator):
    bl_idname = "sync_views.sync"
    bl_label = "Operatorews operator"
    bl_description = "Syncs.syncs across scenes"

    def execute(self, context):
        SyncViews()
        return {'FINISHED'}


def register():
    bpy.utils.register_class(SyncViewsPanel)
    bpy.utils.register_class(SyncViewsOperator)    
def unregister():
    bpy.utils.unregister_class(SyncViewsPanel)
    bpy.utils.unregister_class(SyncViewsOperators)

if __name__ == "__main__":
    register()

yup, that's what I understood from your idea.
You may need to link the camera to the new scene in case it is not ...
(something to try)

One question: do you think this should become an actual C operator? I can make it better of course (to support any camera name, the new render labels, ect), but if this gets implemented natively maybe it's not needed?

hm what do you think? I think it doesn't hurt to have this there. The advantage of python is that you can sync the scene for the lib linked scenes as well (yeah a hack, but python addons can have hacks, C shouldn't). In C we would need to go over the other scenes and if one of the lib linked scenes has a different status all we can do is to report a "warning".