I think there is a misunderstanding of the concept of font manager.
The Font manager acts as a template in our theme, so if you go there and add a name for the template and assign a font it will be available with that name.
So, for example, I will add a template called
This is a Test and assign a font called
Now as this is a Google Font it will also show in the font list of the body in Typography options, but that is not the case for Typekit.
You just need to select THIS IS A TEST and the font type you like will load.
So you did all the settings correctly and added the BODY template name to the typography body option, and in turn, you added to body template the Typekit font. So you are good to go and the front end already shows the correct font.