I have added social icons to my website but I can’t see it when I publish the website
After adding the social icons on your website editor or the header, you need to click on the icons to include URL of your social media pages. You can simply copy the URL of your pages from Facebook, Twitter, Instagram, etc. and paste them on the URL field available for each social icon. Publish your website after these and check again.
You should also check theme options to see if social icons and turned on.