Add production API deployment action

[AetherUnbound]

Description

Follow up to https://github.com/WordPress/openverse-infrastructure/pull/398, this PR adds the production deployment action for the API!

Testing Instructions

Merge and try it out 🙂

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

Developer Certificate of Origin
Version 1.1

Copyright (C) 2004, 2006 The Linux Foundation and its contributors.
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Suite D4700
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Everyone is permitted to copy and distribute verbatim copies of this
license document, but changing it is not allowed.


Developer's Certificate of Origin 1.1

By making a contribution to this project, I certify that:

(a) The contribution was created in whole or in part by me and I
    have the right to submit it under the open source license
    indicated in the file; or

(b) The contribution is based upon previous work that, to the best
    of my knowledge, is covered under an appropriate open source
    license and I have the right under that license to submit that
    work with modifications, whether created in whole or in part
    by me, under the same open source license (unless I am
    permitted to submit under a different license), as indicated
    in the file; or

(c) The contribution was provided directly to me by some other
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    it.

(d) I understand and agree that this project and the contribution
    are public and that a record of the contribution (including all
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    maintained indefinitely and may be redistributed consistent with
    this project or the open source license(s) involved.

[zackkrida]

👍

[github-actions]

Full-stack documentation: Ready

https://WordPress.github.io/openverse/_preview/840

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]

@sarayourfriend if you have the time I've added you as a potential reviewer here, just for the sake of making this update visible to you as someone who architected much of this project. No worries if you can't! Dhruv got it.