So far a "project" is mostly a named session, with various extensions in the past to make it look more like something project.
I, too, would like to change that situation. Store the session part elsewhere (your suggestion is nice), so that the remaining project part is largely static and invariant across systems, so that can be checked in.
Likewise, my goal for the session split is to be able to store geany.conf in my personal "dotfiles" repository that I sync between laptop and workstation.
@elextr @eht16 @b4n is this something you'd agree with? If yes, then we should target that and I'd volunteer to help getting this done.