Foreach Loop Of Post Types With Nested If Else If Not Completing Process

Let’s see if this works. I can’t really test this, but there are some things to update in your code:

function set_activation_value(){
    // Sets Field Defaults
    $option = get_option('ews_index_option_name');
    // get_option returns FALSE if it doesn't exist, so we check that here.
    if ( $option === FALSE ) {

        $args = array (
            'public' => true
        );

        $post_types = get_post_types( $args );
        // Since the option doesn't exist, we should add it, then update it in the loop.
        add_option('ews_index_option_name');
        // now we have an empty array.
        $my_options = [];
        $post_type_output="";
        foreach ( $post_types as $post_type ) {
            // no need to wrap in parenthesis for each condition.
            if ( $post_type === 'page' || $post_type === 'product' || $post_type === 'post' ) {
                $my_options[ $post_type ] = 'index';
                update_option('ews_index_option_name', $my_options);
            // Skip the else if, since every other post type is no index.    
            } else {
                $my_options[ $post_type ] = 'no-index';
                update_option('ews_index_option_name', $my_options);
            }
            $post_type_output .= $post_type;
        }
        // These look to be holding the exact same data on one in an array and the other a string.
        update_option('ews_index_my_types', $post_types);
        update_option('ews_index_option_var', $post_type_output);
    }
}
register_activation_hook( __FILE__, 'set_activation_value' );

I cleaned it up a bit and added comments. Also, there is no reason to have wp_reset_postdata().

As said, I can’t test this, but this might work better for you.