Hope you are doing well, I read your search icon change.
Please follow the steps:
Remove : classes 'medium--hide small--hide' from right icon where 'site-nav__item' class.
Add classed "medium--hide small--hide" in left icon where 'site-nav__item' class.
If you need any help then let me know. Thanks
This will required code change in your theme. If you need assistance to edit theme file to change search icon location please drop me a mail so I can do this for you.