Social Media icons do not work on mobile devices

Mobile compatibility is theme-dependent.

Looking at your site, you use spacious-pro theme.

Since you use a commercial theme and need support, please go to their official support channel. In order to be good stewards of the WordPress community, and encourage innovation and progress, we feel it’s important to direct people to those official locations: https://themegrilldemos.com/spacious-pro/

Forum volunteers are also not given access to commercial products, so they would not know why your commercial theme or plugin is not working properly. This is one other reason why volunteers forward you to the commercial product’s vendors. The vendors are responsible for supporting their commercial product. Commercial products are not supported in these forums.

FYI the icons are visible on my Android phone (Chrome browser).

They are visible, not clickable.

Ah, I see. I cannot click even on desktop (Chrome). There’s another transparent element that overlays the icons, making them unreachable to mouse or tap. This element appears to be a theme feature that you’re not using. If it’s not needed, hiding (different from being transparent) it will make the icons accessible.

.header-sidebar-wrapper {
  display: none;
}

Add to the Additional CSS customizer section.

This is a “band-aid” solution. It’d be better for your theme’s devs to resolve this properly for you. Their assistance should be part of why you paid for a commercial theme and why t-p’s reply remains pertinent.