There are two ways how libraries are provided: The old way and the new way.

In the old way, addons would include all the libraries they need to run, so you only have to install the addon and everything is there. While this seems convenient, it causes problems if multiple addons need the same library, but provide it in a different version. The game will then load that library version, whose parent addon is loaded first.

In the new way, addons do not include any libraries and instead they need to be installed separately. While this initially looks more complicated, it actually solves all the problems from the old way. If all addons are following the new way, all addons will always use the latest version of the library and there is no conflict anymore.


So, if you have the latest (standalone) library version installed, but PersonalAssistant (or any other addon) is telling you that you need a newever version of a library, then you most likely have another addon installed, that still does it the old way and includes an older version of the library in itself.
In order to resolve this issue, you can do two things:

1. Immediate fix is to go through all addons you have installed and check if they contain a sub-folder with the same name as the library that the game tells you is outdated. If you find it, delete that folder (the library, not the addon :o)
2. Contact the author of that addon and tell him/her that libraries should no longer be included in his addon, but installed standalone.

Further readings on this topic:

• Let's get rid of LibStub! (esoui forum)
• Libraries (esoui wiki)