Backport of Move writing of stored keys to the end of Vault initialization. into release/1.17.x

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

Backport

This PR is auto-generated from #28538 to be assessed for backporting due to the inclusion of the label backport/1.17.x.

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

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Description

Move the call to SetStoredKeys to the end of the initialization process. On Vault Enterprise, this minimizes the chances that the initial seal re-wrap fails when a node other than the one performing initialization becomes the active one.

TODO only if you're a HashiCorp employee

• Backport Labels: If this PR is in the ENT repo and needs to be backported, backport
  to N, N-1, and N-2, using the backport/ent/x.x.x+ent labels. If this PR is in the CE repo, you should only backport to N, using the backport/x.x.x label, not the enterprise labels.
  • If this fixes a critical security vulnerability or severity 1 bug, it will also need to be backported to the current LTS versions of Vault. To ensure this, use all available enterprise labels.
• ENT Breakage: If this PR either 1) removes a public function OR 2) changes the signature
  of a public function, even if that change is in a CE file, double check that
  applying the patch for this PR to the ENT repo and running tests doesn't
  break any tests. Sometimes ENT only tests rely on public functions in CE
  files.
• Jira: If this change has an associated Jira, it's referenced either
  in the PR description, commit message, or branch name.
• RFC: If this change has an associated RFC, please link it in the description.
• ENT PR: If this change has an associated ENT PR, please link it in the
  description. Also, make sure the changelog is in this PR, not in your ENT PR.

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Overview of commits

• e7e16fd

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CI Results:
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