But the license prohibits competitive use, not commercial use, right? So using Vault in production is no problem if you're using it as part of the infrastructure of a company that isn't competing with Hashicorp.
Using it as a backend for a password manager... more of a grey area, but Hashicorp doesn't offer a password manager.
Oh, for sure, and if you're a developer tooling/devopsy-stuff company that would give me pause (or convince me to plan a migration, or to use an alternative, etc.)
But if you're, say, fashion retail, or something, then the risk is pretty low.