[EngSys] API-doc preview fails on release branches missing GitHub App fix

## Impact

The `spec - api-doc-preview` Azure Pipeline fails before checkout for pull requests targeting release branches that predate the GitHub App migration in Azure/azure-rest-api-specs#45023.

Confirmed affected builds on 2026-07-28:

- PR Azure/azure-rest-api-specs#44927: builds 6627189, 6627236, 6627266
- PR Azure/azure-rest-api-specs#45060: builds 6627360 and 6627409

## Corrected root cause

This is not a repository-wide outage on current `main`.

- `main` contains approved commit `dac076369edef5252b3e871da5cd37ba99eff91b` from Azure/azure-rest-api-specs#45023.
- That change mints distinct GitHub App installation tokens for `Azure` commit statuses and `MicrosoftDocs/AzureRestPreview` checkout/push.
- Its API-doc check succeeded in build 6623677.
- The affected release branches were cut before #45023 and still invoke legacy `$(azuresdk-github-pat)`, which now returns HTTP 401.

The first failing step reports:

```text
"message": "Bad credentials"
"status": "401"
gh: Bad credentials (HTTP 401)
```

Later missing `.github/shared` errors are cascades because checkout never ran.

## Resolution

Backport commit `dac076369edef5252b3e871da5cd37ba99eff91b` to each affected release branch rather than rotating or reintroducing the PAT.

For the July AKS branch:

- Backport: signed commit `0aebd856aecbdb786ea12ac2600bd5ddade5bfd0`
- Rebased focused FIPS head: signed commit `f68ba70a075245429f911a874060f0cd47ac05e1`
- Validation build: 6627583

PR #45060 remains one commit and seven FIPS files; the pipeline fix lives only on its base branch.