This is one of the other jobs of a notary: not vouching for identity, but rather signing off on a document stating that a collection of associated objects are what is described in the document.
Such a document has the same sort of purpose as a certificate of authenticity you'd get from an appraiser; but you use a notary in cases where the thing doesn't need authentication to be valuable, instead being a liquid asset with a clear market value. The notary doesn't write down such a value, or even know it; they just sign off on a description of the item, knowing that the value can later be readily determined from the description by any interested party.
Of course, to make this work, you need the notary to sign off on the contents of the collection right before you secure the collection into storage. Otherwise, you could just make arbitrary alterations to the contents yourself. For this reason—and because notaries don't usually like getting dragged all around town to vouch for things—usually a bank will retain the services of notary of their own, and offer it to safe-deposit-box users as an option. If a notary is used to vouch for the contents on first deposit, then a notary must be used on all further deposits/withdrawals to "retain the chain of custody." This turns the safe deposit box into a managed safe-deposit service.