Add a private secret manager example and test

[kierramarie]

Description

A private only secrets manager example needs to be created and used in a test in the pr_test.go.

New or affected modules

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[ocofaigh]

@kierramarie instead of adding a whole new example, maybe update one of the existing ones to deploy private only since we already have 2 examples

[kierramarie]

PR merged. Closing issue.