Backport of run integration tests on push in main and release/* into release/1.19.x (#21667)

* backport of commit cb63abf7a7

* backport of commit 40a95ae759

---------

Co-authored-by: John Murret <john.murret@hashicorp.com>

.github/workflows/test-integrations.yml

@@ -13,6 +13,11 @@ on:
       - 'backport/docs/**'
       - 'backport/ui/**'
       - 'backport/mktg-**'
+  push:
+    branches:
+      # Push events on the main branch
+      - main
+      - release/**
 
 env:
   TEST_RESULTS_DIR: /tmp/test-results