The Geyser project is a re-imagining of the old Spout project that extended what Bukkit plugins were capable of by using client-side mods. Geyser Recipes is the first in the Geyser suite of mod/plugins that will aim to do the same, extend what Bukkit plugins are capable of doing.
Geyser Core provides some information to the server about your client installation, mainly which mods part of the Geyser suite you have installed as well as some common code used between the various Geyser mods. Has no effect unless the Geyser Core Bukkit plugin is also installed on the server.
Any questions or discussion can be held in the #geyser channel on the Selim Modding Discord server.