### 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
for (int i = 0; i < editor_data.get_edited_scene_count(); i++) {
		if (editor_data.get_scene_path(i) == p_path) {
			return true;
		}
	}
	return false;
}
void EditorNode::fix_dependencies(const String &p_for_file) {
	dependency_fixer->edit(p_for_file);
}
int EditorNode::new_scene() {
	int idx = editor_data.add_edited_scene(-1);
	_set_current_scene(idx); 
	
	if (editor_data.get_edited_scene_count() > 1) {
		for (int i = 0; i < editor_data.get_edited_scene_count() - 1; i++) {
			bool unsaved = EditorUndoRedoManager::get_singleton()->is_history_unsaved(editor_data.get_scene_history_id(i));
			if (!unsaved && editor_data.get_scene_path(i).is_empty() && editor_data.get_edited_scene_root(i) == nullptr) {
				editor_data.remove_scene(i);
				idx--;
			}
		}
	}
	editor_data.clear_editor_states();
	scene_tabs->update_scene_tabs();
	return idx;
}
Error EditorNode::load_scene(const String &p_scene, bool p_ignore_broken_deps, bool p_set_inherited, bool p_clear_errors, bool p_force_open_imported, bool p_silent_change_tab) {