### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
EditorPlugin::AfterGUIInput after = EditorPlugin::AFTER_GUI_INPUT_PASS;
	for (int i = 0; i < plugins_list.size(); i++) {
		if ((!serve_when_force_input_enabled) && plugins_list[i]->is_input_event_forwarding_always_enabled()) {
			continue;
		}
		EditorPlugin::AfterGUIInput current_after = plugins_list[i]->forward_3d_gui_input(p_camera, p_event);
		if (current_after == EditorPlugin::AFTER_GUI_INPUT_STOP) {
			after = EditorPlugin::AFTER_GUI_INPUT_STOP;
		}
		if (after != EditorPlugin::AFTER_GUI_INPUT_STOP && current_after == EditorPlugin::AFTER_GUI_INPUT_CUSTOM) {
			after = EditorPlugin::AFTER_GUI_INPUT_CUSTOM;
		}
	}
	return after;
}
void EditorPluginList::forward_canvas_draw_over_viewport(Control *p_overlay) {
	for (int i = 0; i < plugins_list.size(); i++) {
		plugins_list[i]->forward_canvas_draw_over_viewport(p_overlay);
	}
}
void EditorPluginList::forward_canvas_force_draw_over_viewport(Control *p_overlay) {
	for (int i = 0; i < plugins_list.size(); i++) {
		plugins_list[i]->forward_canvas_force_draw_over_viewport(p_overlay);
	}
}
void EditorPluginList::forward_3d_draw_over_viewport(Control *p_overlay) {