The situation is the same for me. openedx-language-preference is set on the lms dashboard as seen in the picture.

But on the mfe profile page there are no cookies set at all. Here is the Network console:
The situation is the same for me. openedx-language-preference is set on the lms dashboard as seen in the picture.

But on the mfe profile page there are no cookies set at all. Here is the Network console: