Remove deprecated Elastic analytics plugin

The Elastic Search UI analytics plugin has been deprecated: https://www.npmjs.com/package/@elastic/search-ui-analytics-plugin

There's not a clear replacement for it, but it just might be this: https://www.npmjs.com/package/@elastic/behavioral-analytics-javascript-tracker

There are some docs here, but they seem outdated since they don't mention the deprecation: https://www.elastic.co/guide/en/search-ui/current/api-core-plugins-analytics-plugin.html

We should:

• Determine if it's worth keeping behavioral analytics at all. Is it doing anything we're not already capturing with Google Analytics? (Search analytics via Google): https://lookerstudio.google.com/reporting/d6af7a2b-2aaa-4f30-8742-811e62777c93/page/p_0k9jmllz6c
• If it's worth keeping the extra analytics, we'll need to drop the deprecated plugin and refactor accordingly.
• Or, if we decide to drop it, remove the code, docs, and env variables that support it.