Hello,
I chose External file https://prnt.sc/1tc53sh and also regenerated files https://prnt.sc/1tc4zr6 and menu looks ok for both pages.
Yes, you can use Loco translate to translate theme and core plugin but don’t use Author directory, only System or Custom https://prnt.sc/1tc57jz . In other case, you will lose translation after the theme or plugin update.
Regards
