Remove the fallback implementations when WP_HTML_Tag_Processor is available in core (6.2)

[matiasbenedetto]

When WP_HTML_Tag_Processor is available in WordPress core (6.2), we could remove the fallback implementation of dom parsing using DOMDocument and/or regex introduced in this PR #213 to circumvent the lack of that tool when Gutenberg is not installed.

[pbking]

Complete. :) Done with 2.0 release which raised requirements to WordPress 6.5