On Tokyo demo’s homepage the header is manually adjusted in width, inside the Header – Homepage global section . Try to click on the bottom left gear and adjust the header’s width (entire container, not just its inner section).
Quick video recording here https://d.pr/v/aOWeBg .
Yes, there 2 headers, one for the Homepage which looks more minimal with the menu as a hamburger, and another header for the rest of the website, that’s fully stretched.
The general global header is set in Customizer > Header > General, while the homepage one is set in the Homepage’s backend settings eg: https://d.pr/i/E86DvK .
Both Header global sections can be edited in Rey theme > Global sections in the backend.
Simply try editing the Hover panels cover, parent section and change its background eg: https://d.pr/i/oaXIx8 .