LCP, FCP and custom post type template give me a headache.

Can you link us to the page?

1. Use HTTP/2, please check with your host service.

2. For the hero image, use a smaller image on mobile, try this PHP code:

function db_modify_srcset_sizes($sizes, $size) {
        $sizes = '(max-width: 420px) 280px, (min-width: 421px) 600px, (min-width: 769px) 1080px, 100vw';
	return $sizes;
}
add_filter('wp_calculate_image_sizes', 'db_modify_srcset_sizes', 10 , 2);

Adding PHP: https://docs.generatepress.com/article/adding-php/

OR

Add another dynamic image just for mobile only, and select medium size for the image.
Hide the original featured image by adding hide-on-mobile class, and hide the new one by adding hide-on-tablet, hide-on-desktop classes.

Adding CSS class(es): https://wordpress.com/support/wordpress-editor/adding-additional-css-classes-to-blocks/

3. You can preload the featured image by adding this PHP code:

// In your theme's functions.php or a custom plugin
function preload_featured_image() {
    if ( is_single() || is_page() ) {
        $featured_image_url = get_the_post_thumbnail_url( get_the_ID(), 'full' );
        if ( $featured_image_url ) {
            echo '<link rel="preload" href="' . esc_url( $featured_image_url ) . '" as="image"/>';
        }
    }
}
add_action( 'wp_head', 'preload_featured_image' );