You say that we can not use different code for desktop, mobile and tablet view???
You can, of course. If you want you can create as many different search bars with different configurations and use different shortcodes. If your theme supports different blocks for different views, then it’s easy – most themes do support that.
Usually a different shortoce is used for mobile/desktop views if you want a completely different layout. That is super simple to do, most themes do support that.
I would put the [wd_asp id=1] with the custom CSS into the header, then use [wd_asp id=2] in the mobile view, and then you can style them differently as you need.