Kindly try setting a logo in Appearance > Customize > Layout > Header as well, in the Mobile Header section.
As for the padding, you may go to Appearance > Customize > Layout > Container > Content Padding and modify the value of the Top padding. Try making it 0 for instance on mobile view: https://share.getcloudapp.com/8LuD1n54
Logo replacement worked great. But space reduction, shows perfect on preview on the website and I saved it and I even cleared WPEngine cache – but it still look the same on mobile with too much space. Can you send me screenshot from your mobile so I can see how it looks on your mobile please? I don’t know why space did not reduce itself on mobile as it looks good on preview on the website as I was reducing padding to zero like you suggested.
It works on mobile well now also. Please ignore above message. Last question. How do I get rid off author names from showing on attention.cc. I highlight in yellow on the screenshot what I am talking about: https://pasteboard.co/wlWkwPLWnwwG.png