There are 2 different library download/install issues.
Encore CS6 installs with no library. The “functional content” install you describe having is step one. It installs an Encore library and styles (and some other content for Premiere), but that library consists of only a few templates, and not the full library with buttons, etc.
If you went to this link:
https://helpx.adobe.com/x-productkb/multi/library-functional-content-missing.html
you can find the additional library content (more tempaltes, the buttons, etc) in the section lower on that page which says “Additional Solution: Install the Resource Central library content.”
The same files with the buttons can also be located from this link:
https://helpx.adobe.com/encore/using/download-library-content.html
The process involves a “double extraction” of compressed files – the downloaded file is a .zip; when you extract it, you have another compressed file, a .7z. Just follow the instructions at the link.
Stan Jones