[VAULT-38229] Enable test timing cache restore without requiring cache updates in nightly tests

[brewgator]

Description

CE portion of https://github.com/hashicorp/vault-enterprise/pull/8469

TODO only if you're a HashiCorp employee

• Backport Labels: If this fix needs to be backported, use the appropriate backport/ label that matches the desired release branch. Note that in the CE repo, the latest release branch will look like backport/x.x.x, but older release branches will be backport/ent/x.x.x+ent.
  • LTS: 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.

PCI review checklist

• I have documented a clear reason for, and description of, the change I am making.
• If applicable, I've documented a plan to revert these changes if they require more than reverting the pull request.
• If applicable, I've documented the impact of any changes to security controls.

Examples of changes to security controls include using new access control methods, adding or removing logging pipelines, etc.

[github-actions]

CI Results:
All Go tests succeeded! ✅

[github-actions]

Build Results:
All builds succeeded! ✅

[tvo0813]

LGTM, other than the pipeline failing