(Feel free to remove this as a subtask!)
We have a straightforward image for ElasticSearch 6 in the releng/dev-images repo added as part of T231864: Create elasticsearch service, this task would have us create a version for ElasticSearch 7.
I suppose that is probably blocked on the availability of the wikimedia/search/extra and wikimedia/search/highlighter/experimental-highlighter-elasticsearch-plugin plugins for ElasticSearch 7, but maybe ElasticSearch 7 without those plugins would be usable in some form?