Warning “Attempt to read property ‘feeds’ on null” using post update function

You’re calling $this->update_product(); too early, I guess just after you’ve constructed the object? It is then calling wp_update_post before everything else has finished loading, in this case the $wp_rewrite global which isn’t available until the setup_theme event.

You should probably call update_product() from the init hook instead:

add_action( 'init', [ $this, 'update_product' ] );