Global headers not displaying properly after update.

Yup so looks like there are some conflicts in display rules as explained in details here:
https://docs.generatepress.com/article/conflicting-display-rules/

Have you done the test I suggested above?

Can you set the status of all header elements to Draft and only keeping the one you are referring to published?

Yep, just done that. I had an "empty homepage header" element that was set to display on the entire site. I've changed the display rules and everything is now working properly!

Thank you so much for your help!

Sorry if I appeared a little bit stressed - I have to show this site to a potential client in about 9 hours from now...

No problem :)