[EuiPageTemplate] Ensure context provides updates to template children

[mgadewoll]

Summary

⚠️ This PR should be rebased with this PR to ensure storybook stories for EuiPageTemplate are available

This PR is a follow-up to an issue noticed here.

EuiPageTemplate did not properly pass down props to the page template subcomponents.
The reason was that changes on the context did not actually trigger updates on the children using that context.

To ensure this, this PR adds a provider wrapper for EuiPageTemplate which ensures that
a) all nested children AND the page template itself correctly consume the context and that
b) there is a state update which triggers context updates inside the consumers.

QA

• ensure that the staging docs for EuiPageTemplate is the same as production
• ensure that the staging storybook for EuiPageTemplate is the same as production (⚠️ waiting for previous PR to be merged for this to be available)

General checklist

• Browser QA
  • Checked in both light and dark modes
  • Checked in mobile
  • Checked in Chrome, Safari, Edge, and Firefox
  • Checked for accessibility including keyboard-only and screenreader modes
• Docs site QA
  • Added documentation
  • Props have proper autodocs (using @default if default values are missing) and playground toggles
  • Checked Code Sandbox works for any docs examples
• Code quality checklist - N/A
• Release checklist
  • A changelog entry exists and is marked appropriately.
  • If applicable, added the breaking change issue label (and filled out the breaking change checklist)

[kibanamachine]

Preview staging links for this PR:

• Docs site: https://eui.elastic.co/pr_7663/
• Storybook: https://eui.elastic.co/pr_7663/storybook

[elasticmachine]

💚 Build Succeeded

• Buildkite Build
• Commit: c2fbd23

[mgadewoll]

We addressed the updates in another PR and changed the approach to prevent having to use stateful wrapper. (link)