There is a problem that I meet is the shipping bar blocks header on mobile. And I saw a few solutions in the community that doesn't work for me.
App: Free Shipping Bar
Kindly share your store URL so,
I can solve it perfectly.
Maybe im not following but it looks like it worked for me. I've refreshed it, clicked search button and the search input is now above it. I also double checked mobile right now and it worked. Try viewing it in incognito mode.