How do I know what OpenWRT version the github it is building on the currently released branch? E.g. Morse 2.2.2 vs Morse 2.6.6, and how do I configure it?
When it’s built the image, it will be in the image name 
You can also check what’s in your .config file or the boards directory (search for CONFIG_VERSION_CODE).
The current open source release cannot build older versions, because we haven’t exposed the whole history. The plan is that you will be able to build future versions… or at least close to.
Note that this is distinct from the OpenWrt version we’re based on, which is currently 23.05.3 (you can see this in the interface, or by looking at the commit history of the openwrt repository before the Morse commits started - see 01170d518da1c8ade9d26e56d0135d12cda8e781).