I am in the process of migrating away from NEST 7.17.5 to Elastic.Clients.Elasticsearch 8.10.0. While most of the code has been migrated, I fail to find a way to get back the functionality of the following functions available in the NEST library:
It seems they have not been ported at all.
Correct. This is the Github issue collecting the list of supported/unsupported APIs for current 8.x client: https://github.com/elastic/elasticsearch-net/issues/7890.
Basically, there's a generic workaround to use low-level client Elastic.Transport: https://www.elastic.co/guide/en/elasticsearch/client/net-api/current/migration-guide.html#_workarounds_for_missing_features. It should work for the cases you listed in your question.