Update deployment actions using new definitions

[AetherUnbound]

Description

Follow up to https://github.com/WordPress/openverse-infrastructure/pull/353 and similar to WordPress/openverse-api#1114

This PR updates the deployment actions to use the new definitions.

Testing Instructions

Merge and find out I suppose! Hard to test GitHub actions on their own.

Checklist

• My pull request has a descriptive title (not a vague title like
  Update index.md).
• My pull request targets the default branch of the repository (main) or
  a parent feature branch.
• My commit messages follow best practices.
• My code follows the established code style of the repository.
• I added or updated tests for the changes I made (if applicable).
• I added or updated documentation (if applicable).
• I tried running the project locally and verified that there are no visible
  errors.

Developer Certificate of Origin

Developer Certificate of Origin

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[github-actions]

Storybook and Tailwind configuration previews: Ready

Storybook: https://wordpress.github.io/openverse-frontend/_preview/2123
Tailwind: https://wordpress.github.io/openverse-frontend/_preview/2123/tailwind

Please note that GitHub pages takes a little time to deploy newly pushed code, if the links above don't work or you see old versions, wait 5 minutes and try again.

You can check the GitHub pages deployment action list to see the current status of the deployments.

[zackkrida]

This looks good

[obulat]

Let's merge and find out :)