I have enabled the new modal Navigation Search as described in the recent announcement:
I deactivated the old one in the Customizer (Customize > Layout > Primary Navigation).
Sorry, I cannot debug using the link you shared, this site is in production. I can’t do this.
What are alternative options to find about this issue, please?
Please note that if you open any page or post on my site, you will see a new search option in the footer without the need to click on the Search icon in the top main menu.
Why it’s showing in the footer?
For the typography you can Add New Typography, set the Target Element to Custom and use the .search-modal-form input class if you want modify the search field typography.