This is an accepted solution.
Aibek is here from Speedimize.io agency.
You have a ready-made hidden-phone class in your theme http://joxi.ru/V2VaNqxTdnR3om. You need to find this element in the editor and add this class.
Most likely, the search is located in header.liquid. Find it there and add a class.
After that, there will be no search on mobile phones.
Hope that helps you.