Backport of Don't exit just because we think there was a possible deadlock into release/1.12.x

[hc-github-team-secure-vault-core]

Backport

This PR is auto-generated from #21342 to be assessed for backporting due to the inclusion of the label backport/1.12.x.

🚨

Warning automatic cherry-pick of commits failed. If the first commit failed,
you will see a blank no-op commit below. If at least one commit succeeded, you
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the merge conflict occurred.

The person who merged in the original PR is:
@ncabatoff
This person should manually cherry-pick the original PR into a new backport PR,
and close this one when the manual backport PR is merged in.

merge conflict error: POST https://api.github.com/repos/hashicorp/vault/merges: 409 Merge conflict []

The below text is copied from the body of the original PR.

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Fixes #21338

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Overview of commits

• f12c128

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[ncabatoff]

Replaced by #21349