Migrate api docs plugin to new system

[camilaibs]

Hey, I just made a Pull Request!

Migrate the api-docs to the new Frontend system,

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:heavy_check_mark: Checklist

• [x] A changeset describing the change and affected packages. (more info)
• [ ] Added or updated documentation
• [ ] Tests for new functionality and regression tests for bug fixes
• [ ] Screenshots attached (for UI changes)
• [x] All your commits have a Signed-off-by line in the message. (more info)

[backstage-goalie[bot]]

Changed Packages

Package Name	Package Path	Changeset Bump	Current Version
example-app-next	packages/app-next	none	v0.0.6-next.2
@backstage/plugin-api-docs	plugins/api-docs	minor	v0.10.4-next.2
@backstage/plugin-catalog	plugins/catalog	patch	v1.17.0-next.2

[github-actions[bot]]

Uffizzi Cluster pr-22752 was deleted.

[github-actions[bot]]

Thank you for contributing to Backstage! The changes in this pull request will be part of the 1.23.0 release, scheduled for Tue, 20 Feb 2024.