Indeed, the link of a
<a> element is right inside of the tag, in the HTML document.
Adding a class is only adding vocabulary, that’s useful to apply styles defined in the CSS document.
<a href="link" class="my-link">
So you can’t ever update the link itself from the CSS file.
Other objects, such as images, can sometimes be part of the HTML (as an image element) or in the CSS (as a background-image property for an element). But not links.
In Webflow, to keep an element updated throughout a page or a site, you can use Symbols (soon to be renamed Components).
Symbols lately got a feature that allow you to style them differently, or have veriation of contents, using Symbol Content Override.
Read about all those topics in Webflow university.