How to display only the excerpt in the blog/posts page with Gutenberg?

You should use a custom page for this. For reference, we can modify the default (twentynineteen) post content block. Depending on your theme, you may need to modify single.php, or a content block included from there. In the twentynineteen theme, we can see this on line 24:

get_template_part( 'template-parts/content/content', 'single' );

Following that, we can look into template-parts/content/content-single.php at line 23:

 23         the_content(
 24             sprintf(
 25                 wp_kses(
 26                     /* translators: %s: Name of current post. Only visible to screen readers */
 27                     __( 'Continue reading<span class="screen-reader-text"> "%s"</span>', 'twentynineteen' ),
 28                     array(
 29                         'span' => array(
 30                             'class' => array(),
 31                         ),
 32                     )
 33                 ),
 34                 get_the_title()
 35             )
 36         );
 37  

So, you could replace this call to the_content with something like this:

the_excerpt(); // Echo the excerpt directly.
$excerpt = get_the_excerpt(); // Store the excerpt in $excerpt.

// Retrieve the "raw" exceprt - this has not passed any filters etc,
// and instead comes directly from the database.
$post = get_post();
echo $post->post_excerpt;