Template part block fails attempting to preview recursive template parts

[bobbingwide]

Describe the bug
For issue #26923 I created a couple of template parts which would cause an infinitely recursive loop.
In Gutenberg 9.5.1 these cause the Template part block to fail with This block has encountered an error and cannot be previewed.

A clear and concise description of what the bug is.

To reproduce
Steps to reproduce the behavior:

1. Using a Full Site Editing theme such as Twenty Twenty-One blocks create recursive template parts as below.
2. Add a new post.
3. Add a Template part block.
4. Click on Choose existing.
5. Wait for a while.
6. The block will fail.

issue-27.html

<ul>
    <li>Issue-27 test case.
    <!-- wp:template-part { "slug": "issue-30", "theme": "fizzie" } /-->
    </li>
</ul>

issue-30.html

<ul>
    <li>Issue-30 test case.
    <!-- wp:template-part { "slug": "issue-27", "theme": "fizzie" } /-->
    </li>
</ul>

Expected behavior

• The fixes developed to prevent recursion in the server need equivalent logic in the block editor.
• The preview should indicate that recursion has occurred, indicating where it was detected.
• It could suggest a method for fixing the problem.

Screenshots

Editor version (please complete the following information):

• WordPress version: [e.g: 5.3.2] 5.6
• Does the website has Gutenberg plugin installed, or is it using the block editor that comes by default? [e.g: "gutenberg plugin", "default"] 9.5.1
• If the Gutenberg plugin is installed, which version is it? [e.g., 7.6]

Desktop (please complete the following information):

• OS: [e.g. iOS] Windows
• Browser [e.g. chrome, safari] Chrome
• Version [e.g. 22] 87.0.4280.88 (Official Build) (64-bit)

Additional context
See also

• Fatal errors due to infinite recursion with Full Site Editing #26923
• The recursive template parts in Fizzie break Gutenberg's Template parts block  bobbingwide/fizzie#49