I am interested in using Project Feather as a standalone CMS independent of Sitefinity but from the documentation it does not appear that Project Feather supports working as a fully-functional standalone CMS.
My original understanding was that ProjectFeather was a free and open-source community project as an alternative for people who did not want to purchase licenses for Sitefinity CMS, however, that does not appear to be the case based on the documentation.
Is it possible to run Project Feather as a standalone CMS or will it always be dependent on the structure of Sitefinity CMS and the licensing restrictions of Sitefinity?
No, your understanding of what it was was incorrect...it's not like anything has changed.
Feather isn't a CMS...it's just a better modern front-end framework (set of tools) for Sitefinity...so it's open source so you can contribute to it, but it still requires Sitefinity. They never claimed otherwise, know what I mean?