[docs] Add the new docs CI checks

[colleenmcginnis]

In #9440, we're going to start publishing release notes from this repo instead of manually copy and pasting them into the elastic/docs-content repo. This PR adds the docs CI checks necessary to build docs previews.

cc @elastic/docs-engineering @ebeahan

[mergify]

This pull request does not have a backport label. Could you fix it @colleenmcginnis? 🙏
To fixup this pull request, you need to add the backport labels for the needed
branches, such as:

• backport-./d./d is the label that automatically backports to the 8./d branch. /d is the digit
• backport-active-all is the label that automatically backports to all active branches.
• backport-active-8 is the label that automatically backports to all active minor branches for the 8 major.
• backport-active-9 is the label that automatically backports to all active minor branches for the 9 major.

[elasticmachine]

Pinging @elastic/ingest-docs (Team:Docs)