Is there a way to interpolate CSS variables with url()?

You can perform interpolation with most CSS functions, including rgba() (see an example here). In fact, interpolation is one of the main features of custom properties.

But you cannot do this with url(), as url(var(--url)) is parsed not as a url( function token followed by var(--url) followed by a ), but a single url() token that is invalid because the var(--url) is being treated as a URL itself, and unquoted URLs in url() tokens cannot contain parentheses unless they are escaped. This means the substitution never actually occurs, because the parser never sees any var() expressions in the property value — indeed, your background declaration is completely invalid.

If you didn't understand any of that, that's fine. Just know that you cannot use var() interpolation with url() due to legacy reasons.

Even though the problem depicted in the question is related to the legacy url() token, you cannot do this by building URL tokens out of several var() expressions either, in case you were thinking of trying something like --uo: url(; --uc: ); or --uo: url("; --uc: ");, and background: var(--uo) var(--url) var(--uc);. This is because custom properties cannot contain unmatched string delimiters or parts of url() tokens (called bad URL tokens).

If you want to specify a URL in a custom property, you need to write out the entire url() expression, and substitute that entire expression:

:root {
  --url: url("https://download.unsplash.com/photo-1420708392410-3c593b80d416");
}

body {
  background: var(--url);
}

Or, use JavaScript instead of var() to perform the interpolation.

You cannot interpolate css variables with url but what you can do is to implement the url function as part of your variable like this:

:root {
    --url: url("https://download.unsplash.com/photo-1420708392410-3c593b80d416");
}

body {
    background: var(--url);
}

in HTML could be:

<div class="css_class_setting_background" style=" --url: url("https://download.unsplash.com/photo-1420708392410-3c593b80d416");"> </div>

This works on most of modern browsers.