Private posts and pages are handled as "published"

[millerf]

Steps to reproduce

1. Starting at URL: `posts/{website}
2. Create or modify a "scheduled" post to be "private"
   3 . Got back to the posts page

What I expected

• The post should stay in the "scheduled" tab
• The post should have something showing it is private
• In the search results, the "scheduled" private page doesn't have a "scheduled" label

What happened instead

• The post is in the "published" tab
• There is no sign that it is "private"

Browser / OS version

All

Screenshot / Video

Posts	Search

Context / Source

Same is happening for pages

[millerf]

That was fixed with #41301