Question: how do I set the vault password for a template via the rest api?

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Question

The documentation for setting the vault passphrase on a template via the api docs (both create and edit) mention a template vault type that seems to be the way to set the vault id that contains the vault passphrase. This data type doesn't seem to be corresponding to the values of keys in key stores, and I can't find an incantation that will set this. I've tried many different permutations, mostly as a guess. Right now, the only workaround we have is to set in the UI–this doesn't work for our purposes because we're using the api to generate hundreds of templates for various reasons. If we had to set manually set the vault passphrase in the web view's dropdown for everyone, there's not much point in using the api.

Can you provide some clarity on how to use the TemplateVault type to set the vault key id in a template?

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Web-Backend (APIs)