[8.10] API key authentication for cross-cluster search & detection rules (backport #5447)

[mergify]

Resolves #4796.

No twin PR needed for serverless (not supported yet).

Preview

• Cross-cluster search and detection rules — Updates step 1 to include both auth methods, and also adds some disambiguation in the "Update a rule's API key" section.

Backports

API auth for cross-cluster search was added in 8.10, but it was in beta until 8.14. So we can backport this straight to 8.14, but we should add a beta tag and revise slightly in 8.10–8.13.

We should be able to get Mergify to open the backport PRs for all versions, then manually update the ones where we need the beta tag and revised verbiage. 🤞

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This is an automatic backport of pull request #5447 done by [Mergify](https://mergify.com).

[github-actions]

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