I have the same issue. The cause is that the icon style is wrapped around the link tag and this results in the font to inherit the style from fontawesome.
Also, as it is not embedded in the link it will not render clickable.
I tried adding a font-awesome icon via a reusable block into the menu as a workaround but that block never comes available to be included in the link.
Out of options as this is a plugin we rely on fontawesome to address this issue.
Font awesome should add an input type option.
As <i class=”fa-solid fa-book-open”></i> or as a style element rapped around the element.
Like it is build now it will never work properly with links and that is when it is used the most.