Run the docs checks on pushes to main

.github/workflows/checks.yml

@@ -1,10 +1,16 @@
 name: Docs checks
 
-# No `branches` filter. A stacked pull request targets the branch of the pull
-# request below it, not main, so a `branches: [main]` filter would skip every
-# stacked change and only run on the last one in a stack.
+# No `branches` filter on pull requests. A stacked pull request targets the
+# branch of the pull request below it, not main, so a `branches: [main]` filter
+# would skip every stacked change and only run on the last one in a stack.
+#
+# Also on pushes to main: the translation sync commits straight to main, so a
+# translated identifier that lands there would otherwise show up only on the
+# next unrelated pull request. Running here makes main red when main is red.
 on:
   pull_request:
+  push:
+    branches: [main]
 
 # Read-only. This workflow runs code from the pull request branch, so it is
 # `pull_request` rather than `pull_request_target` and it is given no write
@@ -21,7 +27,7 @@ jobs:
     name: Locale literals and extraction-hostile markdown
     runs-on: ubuntu-latest
     steps:
-      - name: Check out the pull request branch
+      - name: Check out the branch
         uses: actions/checkout@v4
 
       - name: Set up Node 22