[DEVOPS-1750] Fix release Go SDK pipeline (#642)

## Type of change

<!-- (mark with an `X`) -->

```
- [x] Bug fix
- [ ] New feature development
- [ ] Tech debt (refactoring, code cleanup, dependency upgrades, etc)
- [x] Build/deploy pipeline (DevOps)
- [ ] Other
```

## Objective

<!--Describe what the purpose of this PR is. For example: what bug
you're fixing or what new feature you're adding-->

## Code changes

<!--Explain the changes you've made to each file or major component.
This should help the reviewer understand your changes-->
<!--Also refer to any related changes or PRs in other repositories-->

- **.github/workflows/release-go.yml:** Use `bitwarden-devops-bot` PAT
to checkout `sm-sdk-go` repo.

## Before you submit

- Please add **unit tests** where it makes sense to do so

.github/workflows/release-go.yml

@@ -1,4 +1,5 @@
-name: Release Go
+name: Release Go SDK
+run-name: Release Go SDK ${{ inputs.release_type }}
 
 on:
   workflow_dispatch:
@@ -15,6 +16,7 @@ on:
 env:
   GO111MODULE: on
   GO_VERSION: "^1.18"
+  _KEY_VAULT: "bitwarden-ci"
 
 jobs:
   validate:
@@ -47,7 +49,6 @@ jobs:
     runs-on: ubuntu-22.04
     needs: validate
     env:
-      _KEY_VAULT: "bitwarden-ci"
       _BOT_EMAIL: 106330231+bitwarden-devops-bot@users.noreply.github.com
       _BOT_NAME: bitwarden-devops-bot
       _PKG_VERSION: ${{ needs.validate.outputs.version }}
@@ -57,13 +58,6 @@ jobs:
         with:
           path: sdk
 
-      - name: Checkout SDK-Go repo
-        uses: actions/checkout@3df4ab11eba7bda6032a0b82a6bb43b11571feac # v4.0.0
-        with:
-          repository: bitwarden/sm-sdk-go
-          path: sm-sdk-go
-          ref: main
-
       - name: Login to Azure - Prod Subscription
         uses: Azure/login@92a5484dfaf04ca78a94597f4f19fea633851fa2 # v1.4.7
         with:
@@ -76,6 +70,14 @@ jobs:
           keyvault: ${{ env._KEY_VAULT }}
           secrets: "github-pat-bitwarden-devops-bot-repo-scope"
 
+      - name: Checkout SDK-Go repo
+        uses: actions/checkout@3df4ab11eba7bda6032a0b82a6bb43b11571feac # v4.0.0
+        with:
+          repository: bitwarden/sm-sdk-go
+          path: sm-sdk-go
+          ref: main
+          token: ${{ steps.retrieve-secrets.outputs.github-pat-bitwarden-devops-bot-repo-scope }}
+
       - name: Setup Git
         working-directory: sm-sdk-go
         run: |