Only publish release-tag docs on beta channel (#15158) (#15167)

(cherry picked from commit 819d829c41)

Co-authored-by: Tyera Eulberg <teulberg@gmail.com>

docs/build.sh

@@ -17,9 +17,15 @@ source ../ci/rust-version.sh
 # Build from /src into /build
 npm run build
 
-# Publish only from merge commits and release tags
+eval "$(../ci/channel-info.sh)"
+
+# Publish only from merge commits and beta release tags
 if [[ -n $CI ]]; then
   if [[ -z $CI_PULL_REQUEST ]]; then
+    if [[ -n $CI_TAG ]] && [[ $CI_TAG != $BETA_CHANNEL* ]]; then
+      echo "not a beta tag"
+      exit 0
+    fi
     ./publish-docs.sh
   fi
 fi