We do not use Font Awesome 6. CB is still Font Awesome 4. We likely will not be replacing this until CB 3.x when we replace Bootstrap with Tailwind since I'll have to redo all the HTML at that point anyway it'd be a good time.
So you either need to keep both enabled or you need to be sure you're loading Font Awesome 6 backwards compatibility script, which I think might be included with core Font Awesome 6 by default now but I don't know if Joomla 5 is including it.
As for what we plan to replace Font Awesome with it's still undecided (probably
heroicons
), but ideally a more stable icon library as Font Awesome changing icon names every major release is too problematic for us.