Magento 2.4 – Move product-add-form to customer div class

is there any way to move the “product-add-form” to a new customer class?

i have added in the catalog_product_view.xml

<move element="product.add.form" destination="product.info.rechts" before="-"/>

but not working…

PriceBox and Social Links are working…

<move element="product.info.price" destination="product.info.rechts" before="-"/>
<move element="product.info.social" destination="product.info.rechts" after="-"/>

Any idea? Thanks so much
Alex