### 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
if (InspectorDock::get_inspector_singleton()) {
		InspectorDock::get_inspector_singleton()->update_tree();
	}
}
void EditorNode::_editor_select_next() {
	int editor = _get_current_main_editor();
	do {
		if (editor == editor_table.size() - 1) {
			editor = 0;
		} else {
			editor++;
		}
	} while (!main_editor_buttons[editor]->is_visible());
	editor_select(editor);
}
void EditorNode::_open_command_palette() {
	command_palette->open_popup();
}
void EditorNode::_editor_select_prev() {
	int editor = _get_current_main_editor();
	do {
		if (editor == 0) {
			editor = editor_table.size() - 1;
		} else {
			editor--;
		}
	} while (!main_editor_buttons[editor]->is_visible());
	editor_select(editor);
}
Error EditorNode::load_resource(const String &p_resource, bool p_ignore_broken_deps) {