Hi, I just ran into this same issue. This fixed it for me:
Codes and scripting is way over my head, this is how I did it: to apply a script, go to Dashboard > Settings > Custom Code > Add custom code under the Head section. I copied in the code and tweaked the numbers in the code until I was happy (38px for me).
Note for whatever reason this won’t show up in the site editor, so site editing and preview still has the enlarged header, but it displays correctly when I publish & view site that way.
Today randomly my header and doubled in size and lost its background. I used to have my header smaller, but it would refuse to shrink past 54px, like you, I deleted everything in the header, still not budging past 54. Wix phone support spent 30+ mins and couldn’t solve it either.
Hope Wix fixes this soon.