Add workflow to trigger self-host unified build in publish web (#14268)

.github/workflows/publish-web.yml

@@ -141,3 +141,36 @@ jobs:
 
       - name: Log out of Docker
         run: docker logout
+
+  self-host-unified-build:
+    name: Trigger self-host unified build
+    runs-on: ubuntu-22.04
+    needs:
+      - setup
+    steps:
+      - name: Log in to Azure - CI subscription
+        uses: Azure/login@e15b166166a8746d1a47596803bd8c1b595455cf # v1.6.0
+        with:
+          creds: ${{ secrets.AZURE_KV_CI_SERVICE_PRINCIPAL }}
+
+      - name: Retrieve GitHub PAT secrets
+        id: retrieve-secret-pat
+        uses: bitwarden/gh-actions/get-keyvault-secrets@main
+        with:
+          keyvault: "bitwarden-ci"
+          secrets: "github-pat-bitwarden-devops-bot-repo-scope"
+
+      - name: Trigger self-host build
+        uses: actions/github-script@60a0d83039c74a4aee543508d2ffcb1c3799cdea # v7.0.1
+        with:
+          github-token: ${{ steps.retrieve-secret-pat.outputs.github-pat-bitwarden-devops-bot-repo-scope }}
+          script: |
+            await github.rest.actions.createWorkflowDispatch({
+              owner: 'bitwarden',
+              repo: 'self-host',
+              workflow_id: 'build-unified.yml',
+              ref: 'main',
+              inputs: {
+                use_latest_core_version: true
+              }
+            });