The CodePen is https://codepen.io/ericg_off/pen/wvORewY
The CSS is:
.fa-test {
font-family: "Font Awesome 6 Free";
}
The HTML is:
<link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.5.1/css/all.min.css" rel="stylesheet">
<div class="fa-test">

</div>
<div class="fa-test">

</div>
The CodePen result looks like:
FontAwesome does show f3c5 (location-dot) as a free icon...
The other free icon I am using, f007 (user), does work.
Where it gets a bit stranger is that if I use this same code with a Stack Overflow snippet, the location-dot icon will show up.
.fa-test {
font-family: "Font Awesome 6 Free";
}
<link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.5.1/css/all.min.css" rel="stylesheet">
<div class="fa-test">

</div>
<div class="fa-test">

</div>
What needs to change about how I am using CodePen so the free location-dot icon will show up when using FontAwesome 6.5.1?
Set font-weight to 900 in your css class.