Remove permalink-based features from nonpublic CPTs

[johnwatkins0]

Description

Fixes #12008.
Using the released version of the plugin, I came across the error described in #12008 when enabling the new editor for a non-public CPT with an admin UI. I think that issue has been resolved in this repo (and can probably be closed) since the last release, but I found a few other small things to update for non-public CPTs. This PR makes the following changes:

1. Remove the "View Post" link from the publish post notice in the editor. Now it just says "Post published".
2. Skip the "What's next?" sidebar step for non-public CPT because it only pertains to permalinks, which aren't applicable to nonpublic CPTs. If other content is added to this sidebar in the future, the permalink section can be omitted instead of skipping the sidebar step. With this change, when the user confirms publish, the sidebar goes back to the default view instead of to "What's next?"

How has this been tested?

A failing unit test was resolved, and a new unit test added. Tested in the browser using both a non-public CPT and the built-in post type (where everything should be unchanged).

Checklist:

• My code is tested.
• My code follows the WordPress code style.
• My code follows the accessibility standards.
• My code has proper inline documentation.

[jorgefilipecosta]

Thank you for your contribution @johnwatkins0. The code looks good and tested correctly.