BRE-1355 - Rename Bitwarden Unified to Bitwarden Lite (#17456)

(cherry picked from commit fa563641b2)

.github/workflows/publish-web.yml

@@ -157,11 +157,10 @@ jobs:
       - name: Log out of Docker
         run: docker logout
 
-  self-host-unified-build:
-    name: Trigger self-host unified build
+  bitwarden-lite-build:
+    name: Trigger Bitwarden Lite build
     runs-on: ubuntu-22.04
-    needs:
-      - setup
+    needs: setup
     permissions:
       id-token: write
     steps:
@@ -182,7 +181,7 @@ jobs:
       - name: Log out from Azure
         uses: bitwarden/gh-actions/azure-logout@main
 
-      - name: Trigger self-host build
+      - name: Trigger Bitwarden Lite build
         uses: actions/github-script@ed597411d8f924073f98dfc5c65a23a2325f34cd # v8.0.0
         with:
           github-token: ${{ steps.retrieve-secret-pat.outputs.github-pat-bitwarden-devops-bot-repo-scope }}
@@ -190,7 +189,7 @@ jobs:
             await github.rest.actions.createWorkflowDispatch({
               owner: 'bitwarden',
               repo: 'self-host',
-              workflow_id: 'build-unified.yml',
+              workflow_id: 'build-bitwarden-lite.yml',
               ref: 'main',
               inputs: {
                 use_latest_core_version: true