Remember when lightning struck the Salt Lake City Mormon Temple a couple years ago, and the Angel Moroni fell off? Apparently, that's not the whole story; the whole temple nearly fell. They are now semi-secretly rebuilding it (they are calling it "renovations"), and the workers found a giant network of tunnels underneath the temple.
Start at 11:15 in this video: https://www.youtube.com/watch?v=YDf_ymNRk6E
The tunnels do not connect to the vault. It's about 20 miles away and in a canyon in the mountains. The tunnels are all downtown connecting church-owned buildings and parking garages.
Just was a thought, this link has a map of tunnels from 1911, and doesn't show the vault https://utahstories.com/2010/08/what-lies-beneath/
TBH there is more than one vault. Usually when they talk about "The Vault" they are talking about a series of large rooms carved out of solid granite in one of the canyons. (Same granite deposit that was used in the building of the Temple). Space in this vault is rented for the off-site storage of back-up tapes from all over the world.
In the Church administration building there is also one, (or more), "vaults" which contain archives and items of importance in church history. These vaults are closed to the public, but may be connected by the tunnel network.