I’m pretty sure Stacks only includes the free version of FA5. It looks like the icon you’re trying to use is in the “pro” set. I rarely use FA, and it has grown so massive with tons of icons divided into a number of different versions (4/5/6) and sub-versions (free vs pro) that it’s hard to follow.
This is not how, or where you’d place your custom icons. The icon HTML you’ve copied would go in your content. Try for instance a Paragraph or HTML tool as an example.
Also the code you pasted in for a Bootstrap icon, but you’re asking about FontAwesome, which has different code. You’ll need to decide which you want to use and select the appropriate library as pointed out by @Fuellemann above.
After deciding on the library you then would get the appropriate code or use the Icons tool for your icon.