How can I filter image HTML to add schema.org attributes?

works_secondary-image_thumbnail_html is not a WordPress core hook, so your code never executes.

As long as images are displayed on your site by calling wp_get_attachment_image in your theme, you can add to the attributes by hooking into wp_get_attachment_image_attributes:

add_filter( 'wp_get_attachment_image_attributes', 'wpse_235266_image_attributes', 10, 3 );

function wpse_235266_image_attributes( $attr, $attachment, $size ) {

    $attr['itemprop'] = 'image';
    return $attr;

}

For images that have been inserted into post content in the visual editor, you’ll need to filter on the get_image_tag hook to change the HTML that is inserted into each post.

add_filter( 'get_image_tag', 'wpse_235266_image_html', 10, 6 );

function wpse_235266_image_html( $html, $id, $alt, $title, $align, $size ) {

    return str_replace( '<img ', '<img itemprop="image" ', $html );

}

Note that this means your existing posts, where the HTML is already saved within the content, will not get your new attributes. You’ll either need to perform a global replace on old post data to make this change or work through your posts in the editor making changes to all images that cause WP to write the HTML into the post content afresh.

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