How to create color shades using CSS variables similar to darken() of Sass?

The new Specification introduces “relative color syntax” where you can do the following

:root {
    --color-primary: #f00; /* any format you want here */
    --color-primary-darker: hsl(from var(--color-primary) h s calc(l - 5%)); 
    --color-primary-darkest: hsl(from var(--color-primary) h s calc(l - 10%)); 
}

The idea is to convert the main color to hsl format and using calc() you adjust the lightness.

There is still no support for this to date so consider the below solution.

You can consider hsl() colors and simply control the lightness:

:root {
    --color:0, 100%; /*the base color*/
    --l:50%; /*the initial lightness*/
    
    --color-primary: hsl(var(--color),var(--l));
    --color-primary-darker: hsl(var(--color),calc(var(--l) - 5%));
    --color-primary-darkest: hsl(var(--color),calc(var(--l) - 10%)); 
}

.button {
    background: var(--color-primary);
    display:inline-block;
    padding:10px 20px;
    color:#fff;
    cursor:pointer;
}

.button:hover,
.button:focus {
    background: var(--color-primary-darker);
}

.button:active {
    background: var(--color-primary-darkest);
}

<span class="button">some text</span>

As a side note, darken() is also doing the same thing:

Makes a color darker. Takes a color and a number between 0% and 100%, and returns a color with the lightness decreased by that amount.