Why position:sticky is not working when the element is wrapped inside another one?

position:sticky consider the parent element to behave as it should be. In your case the parent element has its height defined by the sticky element so there is no room for the element to have a sticky behavior

Add border to better see the issue:

.nav-wrapper {
  position: absolute;
  bottom: 0;
  border: 2px solid;
}

.nav-wrapper nav {
  position: sticky;
  top: 0;
}

body {
  min-height:200vh;
}

<div class="nav-wrapper">
  <nav>
    <a href="#">
      <li>Home</li>
    </a>
    <a href="#">
      <li>About</li>
    </a>
  </nav>
</div>

Now add height to the parent element and see what is happening:

.nav-wrapper {
  position: absolute;
  bottom: 0;
  border: 2px solid;
  height:80vh;
}

.nav-wrapper nav {
  position: sticky;
  top: 0;
}

body {
  min-height:200vh;
}

<div class="nav-wrapper">
  <nav>
    <a href="#">
      <li>Home</li>
    </a>
    <a href="#">
      <li>About</li>
    </a>
  </nav>
</div>

The sticky behavior is working fine because there is enough height on the parent element where the element can be fixed after a specific threshold.

A stickily positioned element is an element whose computed position
value is sticky. It’s treated as relatively positioned until its
containing block crosses a specified threshold (such as setting top to
value other than auto) within its flow root (or the container it
scrolls within), at which point it is treated as “stuck” until meeting
the opposite edge of its containing block.^ref

Related questions:

Why bottom:0 doesn’t work with position:sticky?

If you specify `bottom: 0` for position: sticky, why is it doing something different from the specs?

‘position: sticky’ not working when ‘height’ is defined