Implement simultaneous PR checks for Node.js v20, v24.

Copied from #2006.

.github/workflows/script/check-js-20.sh

@@ -0,0 +1,37 @@
+#!/bin/bash
+set -eu
+
+# Change @types/node to v20 temporarily to check that the generated JS files are correct.
+contents=$(jq '.devDependencies."@types/node" = "^20.0.0"' package.json)
+echo "${contents}" > package.json
+
+npm install
+
+if [ ! -z "$(git status --porcelain)" ]; then
+    git config --global user.email "github-actions@github.com"
+    git config --global user.name "github-actions[bot]"
+    # The period in `git add --all .` ensures that we stage deleted files too.
+    git add --all .
+    git commit -m "Use @types/node v20"
+fi
+
+# Wipe the lib directory in case there are extra unnecessary files in there
+rm -rf lib
+
+# Generate the JavaScript files
+npm run-script build
+
+# Check that repo is still clean.
+# The downgrade of @types/node means that we expect certain changes to the generated JS files.
+# Therefore, we should ignore these changes to @types/node and check for outstanding changes.
+if [[ $(git diff | grep --perl-regexp '^-(?!--)' | grep --count --invert-match --perl-regexp '"@types/node": "\^24') -gt 0 || \
+      $(git diff | grep --perl-regexp '^\+(?!\+\+)' | grep --count --invert-match --perl-regexp '"@types/node": "\^20') -gt 0 ]]
+then
+    >&2 echo "Failed: JavaScript files are not up to date. Run 'rm -rf lib && npm run-script build' to update"
+    git diff
+    exit 1
+fi
+echo "Success: JavaScript files are up to date"
+
+# Clean up changes to package.json, package-lock.json, and lib/*.js.
+git reset --hard HEAD~1