diff --git a/src/wp-includes/html-api/class-wp-html-tag-processor.php b/src/wp-includes/html-api/class-wp-html-tag-processor.php
index 541b5baf0b..79d96dc8be 100644
--- a/src/wp-includes/html-api/class-wp-html-tag-processor.php
+++ b/src/wp-includes/html-api/class-wp-html-tag-processor.php
@@ -242,6 +242,8 @@
  * unquoted values will appear in the output with double-quotes.
  *
  * @since 6.2.0
+ * @since 6.2.1 Fix: Support for various invalid comments; attribute updates are case-insensitive.
+ * @since 6.3.2 Fix: Skip HTML-like content inside rawtext elements such as STYLE.
  */
 class WP_HTML_Tag_Processor {
 	/**
@@ -568,7 +570,14 @@ class WP_HTML_Tag_Processor {
 			 * of the tag name as a pre-check avoids a string allocation when it's not needed.
 			 */
 			$t = $this->html[ $this->tag_name_starts_at ];
-			if ( ! $this->is_closing_tag && ( 's' === $t || 'S' === $t || 't' === $t || 'T' === $t ) ) {
+			if (
+				! $this->is_closing_tag &&
+				(
+					'i' === $t || 'I' === $t ||
+					'n' === $t || 'N' === $t ||
+					's' === $t || 'S' === $t ||
+					't' === $t || 'T' === $t
+				) ) {
 				$tag_name = $this->get_tag();
 
 				if ( 'SCRIPT' === $tag_name && ! $this->skip_script_data() ) {
@@ -580,6 +589,25 @@ class WP_HTML_Tag_Processor {
 				) {
 					$this->bytes_already_parsed = strlen( $this->html );
 					return false;
+				} elseif (
+					(
+						'IFRAME' === $tag_name ||
+						'NOEMBED' === $tag_name ||
+						'NOFRAMES' === $tag_name ||
+						'NOSCRIPT' === $tag_name ||
+						'STYLE' === $tag_name
+					) &&
+					! $this->skip_rawtext( $tag_name )
+				) {
+					/*
+					 * "XMP" should be here too but its rules are more complicated and require the
+					 * complexity of the HTML Processor (it needs to close out any open P element,
+					 * meaning it can't be skipped here or else the HTML Processor will lose its
+					 * place). For now, it can be ignored as it's a rare HTML tag in practice and
+					 * any normative HTML should be using PRE instead.
+					 */
+					$this->bytes_already_parsed = strlen( $this->html );
+					return false;
 				}
 			}
 		} while ( $already_found < $this->sought_match_offset );
@@ -710,15 +738,33 @@ class WP_HTML_Tag_Processor {
 		return true;
 	}
 
+	/**
+	 * Skips contents of generic rawtext elements.
+	 *
+	 * @since 6.3.2
+	 *
+	 * @see https://html.spec.whatwg.org/#generic-raw-text-element-parsing-algorithm
+	 *
+	 * @param string $tag_name The uppercase tag name which will close the RAWTEXT region.
+	 * @return bool Whether an end to the RAWTEXT region was found before the end of the document.
+	 */
+	private function skip_rawtext( $tag_name ) {
+		/*
+		 * These two functions distinguish themselves on whether character references are
+		 * decoded, and since functionality to read the inner markup isn't supported, it's
+		 * not necessary to implement these two functions separately.
+		 */
+		return $this->skip_rcdata( $tag_name );
+	}
 
 	/**
-	 * Skips contents of title and textarea tags.
+	 * Skips contents of RCDATA elements, namely title and textarea tags.
 	 *
 	 * @since 6.2.0
 	 *
 	 * @see https://html.spec.whatwg.org/multipage/parsing.html#rcdata-state
 	 *
-	 * @param string $tag_name The lowercase tag name which will close the RCDATA region.
+	 * @param string $tag_name The uppercase tag name which will close the RCDATA region.
 	 * @return bool Whether an end to the RCDATA region was found before the end of the document.
 	 */
 	private function skip_rcdata( $tag_name ) {
diff --git a/tests/phpunit/tests/html-api/wpHtmlTagProcessor.php b/tests/phpunit/tests/html-api/wpHtmlTagProcessor.php
index 659ffb848e..31430d07a9 100644
--- a/tests/phpunit/tests/html-api/wpHtmlTagProcessor.php
+++ b/tests/phpunit/tests/html-api/wpHtmlTagProcessor.php
@@ -1871,6 +1871,43 @@ HTML;
 		);
 	}
 
+	/**
+	 * @ticket 59292
+	 *
+	 * @covers WP_HTML_Tag_Processor::next_tag
+	 *
+	 * @dataProvider data_next_tag_ignores_contents_of_rawtext_tags
+	 *
+	 * @param string $rawtext_element_then_target_node HTML starting with a RAWTEXT-specifying element such as STYLE,
+	 *                                                 then an element afterward containing the "target" attribute.
+	 */
+	public function test_next_tag_ignores_contents_of_rawtext_tags( $rawtext_element_then_target_node ) {
+		$processor = new WP_HTML_Tag_Processor( $rawtext_element_then_target_node );
+		$processor->next_tag();
+
+		$processor->next_tag();
+		$this->assertNotNull(
+			$processor->get_attribute( 'target' ),
+			"Expected to find element with target attribute but found {$processor->get_tag()} instead."
+		);
+	}
+
+	/**
+	 * Data provider.
+	 *
+	 * @return array[].
+	 */
+	public function data_next_tag_ignores_contents_of_rawtext_tags() {
+		return array(
+			'IFRAME'           => array( '<iframe><section>Inside</section></iframe><section target>' ),
+			'NOEMBED'          => array( '<noembed><p></p></noembed><div target>' ),
+			'NOFRAMES'         => array( '<noframes><p>Check the rules here.</p></noframes><div target>' ),
+			'NOSCRIPT'         => array( '<noscript><span>This assumes that scripting mode is enabled.</span></noscript><p target>' ),
+			'STYLE'            => array( '<style>* { margin: 0 }</style><div target>' ),
+			'STYLE hiding DIV' => array( '<style>li::before { content: "<div non-target>" }</style><div target>' ),
+		);
+	}
+
 	/**
 	 * Ensures that the invalid comment closing syntax "--!>" properly closes a comment.
 	 *