diff --git a/src/wp-includes/block-template.php b/src/wp-includes/block-template.php
index 0a4d85ac718a9..dc0a7c34798d1 100644
--- a/src/wp-includes/block-template.php
+++ b/src/wp-includes/block-template.php
@@ -207,16 +207,14 @@ function _block_template_render_title_tag() {
  *
  * @access private
  * @since 5.8.0
+ * @since 6.6.0 Block template content now runs through a 'the_block_template_html' filter.
  *
- * @global string   $_wp_current_template_id
- * @global string   $_wp_current_template_content
- * @global WP_Embed $wp_embed                     WordPress Embed object.
- * @global WP_Query $wp_query                     WordPress Query object.
+ * @global string $_wp_current_template_content
  *
  * @return string Block template markup.
  */
 function get_the_block_template_html() {
-	global $_wp_current_template_id, $_wp_current_template_content, $wp_embed, $wp_query;
+	global $_wp_current_template_content;
 
 	if ( ! $_wp_current_template_content ) {
 		if ( is_user_logged_in() ) {
@@ -225,10 +223,36 @@ function get_the_block_template_html() {
 		return;
 	}
 
-	$content = $wp_embed->run_shortcode( $_wp_current_template_content );
-	$content = $wp_embed->autoembed( $content );
-	$content = shortcode_unautop( $content );
-	$content = do_shortcode( $content );
+	$content = $_wp_current_template_content;
+
+	/**
+	 * Filters the block template content.
+	 *
+	 * @since 6.6.0
+	 *
+	 * @param string $content The entire block template content.
+	 */
+	$content = apply_filters( 'the_block_template_html', $content );
+	$content = str_replace( ']]>', ']]>', $content );
+
+	// Wrap block template in .wp-site-blocks to allow for specific descendant styles
+	// (e.g. `.wp-site-blocks > *`).
+	return '<div class="wp-site-blocks">' . $content . '</div>';
+}
+
+/**
+ * Parses dynamic blocks from the block template and re-renders them.
+ *
+ * @since 6.6.0
+ *
+ * @global WP_Query $wp_query
+ * @global string   $_wp_current_template_id
+ *
+ * @param string $content Block template content.
+ * @return string Updated block template content.
+ */
+function do_block_template_blocks( $content ) {
+	global $wp_query, $_wp_current_template_id;
 
 	/*
 	 * Most block themes omit the `core/query` and `core/post-template` blocks in their singular content templates.
@@ -257,20 +281,13 @@ function get_the_block_template_html() {
 	) {
 		while ( have_posts() ) {
 			the_post();
+
 			$content = do_blocks( $content );
 		}
-	} else {
-		$content = do_blocks( $content );
+		return $content;
 	}
 
-	$content = wptexturize( $content );
-	$content = convert_smilies( $content );
-	$content = wp_filter_content_tags( $content, 'template' );
-	$content = str_replace( ']]>', ']]&gt;', $content );
-
-	// Wrap block template in .wp-site-blocks to allow for specific descendant styles
-	// (e.g. `.wp-site-blocks > *`).
-	return '<div class="wp-site-blocks">' . $content . '</div>';
+	return do_blocks( $content );
 }
 
 /**
diff --git a/src/wp-includes/class-wp-embed.php b/src/wp-includes/class-wp-embed.php
index 6b9eaa25db7bc..58102f2dfe1b9 100644
--- a/src/wp-includes/class-wp-embed.php
+++ b/src/wp-includes/class-wp-embed.php
@@ -30,6 +30,7 @@ class WP_Embed {
 	 */
 	public function __construct() {
 		// Hack to get the [embed] shortcode to run before wpautop().
+		add_filter( 'the_block_template_html', array( $this, 'run_shortcode' ), 6 );
 		add_filter( 'the_content', array( $this, 'run_shortcode' ), 8 );
 		add_filter( 'widget_text_content', array( $this, 'run_shortcode' ), 8 );
 		add_filter( 'widget_block_content', array( $this, 'run_shortcode' ), 8 );
@@ -38,6 +39,7 @@ public function __construct() {
 		add_shortcode( 'embed', '__return_false' );
 
 		// Attempts to embed all URLs in a post.
+		add_filter( 'the_block_template_html', array( $this, 'autoembed' ), 6 );
 		add_filter( 'the_content', array( $this, 'autoembed' ), 8 );
 		add_filter( 'widget_text_content', array( $this, 'autoembed' ), 8 );
 		add_filter( 'widget_block_content', array( $this, 'autoembed' ), 8 );
diff --git a/src/wp-includes/default-filters.php b/src/wp-includes/default-filters.php
index 1bcd85e79aaf5..073c5f42f2a21 100644
--- a/src/wp-includes/default-filters.php
+++ b/src/wp-includes/default-filters.php
@@ -603,6 +603,14 @@
 // Global styles custom CSS.
 add_action( 'wp_enqueue_scripts', 'wp_enqueue_global_styles_custom_css' );
 
+// Block template.
+add_filter( 'the_block_template_html', 'shortcode_unautop', 7 );
+add_filter( 'the_block_template_html', 'do_shortcode', 8 );
+add_filter( 'the_block_template_html', 'do_block_template_blocks', 9 );
+add_filter( 'the_block_template_html', 'wptexturize' );
+add_filter( 'the_block_template_html', 'wp_filter_content_tags' );
+add_filter( 'the_block_template_html', 'convert_smilies', 20 );
+
 // Block supports, and other styles parsed and stored in the Style Engine.
 add_action( 'wp_enqueue_scripts', 'wp_enqueue_stored_styles' );
 add_action( 'wp_footer', 'wp_enqueue_stored_styles', 1 );
diff --git a/src/wp-includes/media.php b/src/wp-includes/media.php
index c960e44c460f9..38a4c9f2cbe7e 100644
--- a/src/wp-includes/media.php
+++ b/src/wp-includes/media.php
@@ -1843,6 +1843,11 @@ function wp_lazy_loading_enabled( $tag_name, $context ) {
 function wp_filter_content_tags( $content, $context = null ) {
 	if ( null === $context ) {
 		$context = current_filter();
+
+		// For backward compatibility, continue using the 'template' context for the block template.
+		if ( 'the_block_template_html' === $context ) {
+			$context = 'template';
+		}
 	}
 
 	$add_iframe_loading_attr = wp_lazy_loading_enabled( 'iframe', $context );