FFXVI and XIV connection theory

[SilverArrow20XX]

I'm on the side of all the games taking place in the same galaxy.
Interdimensional travel is used to move through space and time to directly connect these planets.
We have evidence of them also existing in the same space though.

The Creator from FFIV The After Years seeded planets all over the galaxy with crystals to gather data, and likely influenced the evolution of similar life everywhere, similar to how the Ancients in Star Trek caused so many humanoid races to exist.

There's also Pupu, who appears in several games, and travels through space rather than the Rift.

An interesting point in Ultima Thule noted that there were many other dragons that also attempted to flee with eggs. Perhaps these dragons were also chased by Omega frames and are the origin of dragons in other FF games, as well as the Shinryu and Omega from FFV.
Though not every Omega is extraterrestrial. XII's was a giant Mimic for example.

Shantotto was experimenting with interdimensional gates in XI, so that's your explanation there.

I like to think everything is canon, though when it comes to crossovers with other series, its best not to think too hard.
Nier is more significant to Nier outside of the direct events of the Raid. Yokai are just a weird thing that exist in XIV, but never come up outside of the event.

When it comes to contrivances, like Ivalice existing in XIV, so similar to XII, I just treat it as coincidence. It exists for fan service, and there doesn't need to be a special connection to another world to cause it. Maybe echoes across dimensions or some such, but it doesn't actually matter.