Untangle Custom Post Types and Custom Taxonomies

[Copons]

Non-standard custom entities are also loaded in Calypso and should be untangled as well.

1. Investigate how custom entities are handled by Calypso and the nav unification.
2. Redirect to the wp-admin version (no feature gaps expected).
3. Include in the holdout test.

[github-actions]

OpenAI suggested the following labels for this issue:

• [Feature Group] Content Management: The issue is related to how custom entities, such as custom post types and taxonomies, are managed within the content management system.
• [Feature] Custom Content Types: The issue specifically pertains to custom post types and their handling in the Calypso interface.
• [Feature] Calypso & wp-admin Navigation: The issue involves navigating between Calypso and wp-admin, indicating the need for unified navigation for custom entities.

[mmtr]

I think this is a duplicate of #97524, which was already closed.