Block Bindings: Add private HTML API subclass with experimental set_inner_html

[sirreal]

Depends on #7348

Uses an implementation from sirreal#9

Trac ticket:

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[github-actions]

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[sirreal]

9691991 extracted to #7754

[sirreal]

This method allows does "naive" inner HTML replacement, where the content that should be inside the node can change the HTML tree beyond the node.

This is also true with the existing implementation so it's not a regression and can be dealt with now or in follow-up work.

[gziolo]

#6838 uses a pattern for a private processor class:

wordpress-develop/src/wp-includes/class-wp-block.php

Lines 338 to 341 in 825f78e

	$bindings_processor_builder = new class(
	'Do not use this, it will not work. It is only here to create a subclass and call the static creator method',
	WP_HTML_Processor::CONSTRUCTOR_UNLOCK_CODE
	) extends WP_HTML_Processor {

[gziolo]

Nice progress here. In #6838, an HTML API subclass was explored to add support for a new Image attribute. It might be interesting to use it as a reference and potentially borrow the unit test when playing with it.

[SantosGuillamot]

I was testing the pull request, and it seems this method is private. If I change it to protected, everything seems to work as expected.

[sirreal]

Thank you! The changes (that I rebased this on) were partially reverted. This method may become public again in #7912.

For now we can make it protected as part of this PR.