What happened to Versus is screamingly obvious in my opinion.
FFXIII and FFXIV were in full production between 2005 and 2009, an elongated process due to the problems they had with the engine. Versus XIII was obviously pencilled in from the start to release some time after XIII because their "edgy alternative" would always need to follow their orthodox mainline entry.
Essentially this means as a project it would have the lowest priority in terms of active production, but tons of time in pre-production/conceping/prototyping... exactly the sort of situation where a single game gets blown out into a putative trilogy because when you don't have the staff to do something, you may as well expand and iterate on what you have in the hopes it will turn into something amazing.
Unfortunately, shit happens. XIII launches late and to a decidedly mixed response, then XIV lays a fucking egg really setting the cat amongst the pigeons. After 18 months of flailing around trying to fix this failed MMO, they eventually decide to throw everything they have into essentially rebuilding the game from the ground up as fast as possible. A hail-mary pass that essentially consigns all their other major projects onto the back burner for the duration.
Especially risky, single-platform products like Versus XIII.
Toriyama meanwhile is keeping the lights on by recycling the FFXIII assets into a cost-effective and heavily outsourced sequel that evidently was never pre-planned as it begins with a hard-reset on the plot of the original.
LR I really wouldn't be shocked to discover if it was built on the bones of the engine variant originally earmarked for V13 given its quasi --open world structure and dynamic TOD/lighting system. Some funding for this would likely seem more logical than V13 given its multi-platform nature and "completing the trilogy" (haha) gimmick.
Long story short, I'd be surprised if a great deal more than what was used for promotional purposes for Versus XIII actually ever existed in code. I'm sure there's stacks of paperwork and concept assets, but beyond some cg and vertical slice proof-of-concepts, it was always vaporware kept alive solely by Nojima's name and corporate standing.
Looking at what was going on elsewhere in the company over the entire duration of its "development", a team of the size neccessary to execute the project would never have been available.