Hello @lessriquelme,
Thank you for reaching out.
The left header menu (in the Center Header style) is assigned through the Customizer > Header > General > Additional Styling & Settings and set the Left Menu option, and this setting is global and not language specific: https://ibb.co/HT0YGNF8.
As far as I know, Polylang doesn’t create separate Customizer settings per language, so any change made there applies site-wide. You may want to check with the Polylang support team to confirm if they have a workaround for this limitation.
If you need to assign a different left menu for each language, you can do it from Appearance > Menus > Manage Locations, and set menus per language: https://ibb.co/h1R9Y7n2.
Hope it helps.
Best Regards