AI Assistant: Fix selected block while using the AI Assistant extension on a nested block

[dhasilva]

Fixes #37518

Proposed changes:

• Adds the blockProp's className to the input, so both elements have the same className and are understood by the editor to be part of the same block when nested.

Other information:

• Have you written new tests for your changes, if applicable?
• Have you checked the E2E test CI results, and verified that your changes do not break them?
• Have you tested your changes on WordPress.com, if applicable (if so, you'll see a generated comment below with a script to run)?

Jetpack product discussion

Does this pull request change what data or activity we track or use?

Testing instructions:

• Go to the block editor
• Add a Columns block with a column in it
• Add an extended block inside the column (a Heading or Paragraph)
• Use the Ask AI Assistant toolbar action to open the input
• Check that the input stays open and the toolbar does not change

A video comparison for reference:

Before:

Peek.2024-05-23.14-52.mp4

After:

Peek.2024-05-23.14-55.mp4

[github-actions]

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  bin/jetpack-downloader test jetpack fix/ai-assistant-inline-extension-nested-input
  

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[github-actions]

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[lhkowalski]

Code looks good and is testing as expected for the presented use case.

The AI Control appears on the right place and stays open:

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It's also working with multiple columns:

.

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I got a buggy position when testing with rows inside a group, we can keep iterating on this: