Update Elastic Cloud terminology

[bmorelli25]

Summary

The Elastic glossary has been updated. We should update how we refer to our products accordingly.

Examples:

• Elasticsearch Service ➡️ Elastic Stack Hosted
• Serverless ➡️ Elastic Cloud serverless or Serverless project (context dependent)
• Ensure we're accurately describing what Elastic Cloud is (see glossary below)

Example pages that will need to be updated:

• https://www.elastic.co/guide/en/observability/current/observability-get-started.html
• https://www.elastic.co/guide/en/apm/guide/current/apm-quick-start.html

TBD

• Confirm with @florent-leborgne that the internal glossary is up to date

Links

Internal glossary.

[colleenmcginnis]

👋 @florent-leborgne can you confirm if "Elasticsearch Service" should be changed to "Elastic Stack Hosted" or "Elastic Cloud Hosted"? It's not clear in the internal glossary doc (it says "Elastic Stack Hosted", but links to "Elastic Cloud Hosted").

[florent-leborgne]

This glossary isn't maintained.
There is an email thread going with marketing & leadership to discuss how we'll rebrand ESS correctly throughout the docs. I'll update as soon as I know.

[colleenmcginnis]

@florent-leborgne is there an update here? I think we've already been replacing Elastic Cloud terminology, but I'm not sure if we've done a full sweep of all docs.

[florent-leborgne]

There is an ongoing issue to track this https://github.com/elastic/platform-docs-team/issues/366

I'll close this one