Inserter: Templates parts and Content block are showing up in the post editor

[youknowriad]

Description

In the post editor, inserting "content" and "template parts" is forbidden. There's no single rootClientId where inserting these is possible. We should consider checking if it's possible to hide these entirely in these situations.

Step-by-step reproduction instructions

1- Open the post editor.
2- Search for "template part" (or content) in the inserter.
3- Notice that you can see the block in the inserter.

Screenshots, screen recording, code snippet

No response

Environment info

No response

Please confirm that you have searched existing issues in the repo.

• Yes

Please confirm that you have tested with all plugins deactivated except Gutenberg.

• Yes

Please confirm which theme type you used for testing.

• Block
• Classic
• Hybrid (e.g. classic with theme.json)
• Not sure