[Backport 8.16] Checkout correct branch of generator (#2537)

(cherry picked from commit ed3cace)

Co-authored-by: Josh Mock <[email protected]>

Author: github-actions[bot]

.github/make.sh

@@ -176,7 +176,7 @@ else
     --rm \
     $product \
     /bin/bash -c "cd /usr/src && \
-      git clone https://$CLIENTS_GITHUB_TOKEN@github.com/elastic/elastic-client-generator-js.git && \
+      git clone --branch $GENERATOR_BRANCH https://$CLIENTS_GITHUB_TOKEN@github.com/elastic/elastic-client-generator-js.git && \
       mkdir -p /usr/src/elastic-client-generator-js/output && \
       cd /usr/src/elasticsearch-js && \
       node .buildkite/make.mjs --task $TASK ${TASK_ARGS[*]}"