This post contains status info on the 4 Kodi add-ons that support Emby playback in Kodi.
Kodi Media Source Info
There are two main ways for Kodi to display media items:
From its internal database using native c/c++ (Syncing)
As a list of ListItems generated by an add-on in Python querying an external server (Dynamic)
There are advantages and disadvantages with both of there when dealing with external sources.
From the internal DB (Syncing)
It is already migrated, but you need to install it from beta repository, called "Emby-next-gen"