Execute browser tests for pushes to main and all PRs (#17796)

...instead of just pushes to any branch.

Fixes https://github.com/github/docs-internal/issues/17068

.github/workflows/browser-test.yml

@@ -3,6 +3,9 @@ name: Browser Tests
 on:
   workflow_dispatch:
   push:
+    branches:
+      - main
+  pull_request:
 
 jobs:
   see_if_should_skip: