Add Wishlist Product API doesn’t seem to work

I’m moving a WooCommerce shop to a headless setup, so I was happily surprised this plugin offers REST API support!

I can retrieve a wishlist by user or share_key, but adding products to a wishlist doesn’t seem to work.

I’m sending a POST request to /wp-json/wc/v3/wishlist/share_key/add_product with the following JSON body:

{
    "product_id": 36
}

The share_key I use and the product id are correct and to be sure I tried different products. But on every request I get the following response:

{
    "code": "ti_woocommerce_wishlist_api_wishlist_products_not_found",
    "message": "Add product to wishlist failed.",
    "data": {
        "status": 400
    }
}

I see more than 1 user with the same issue:

https://www.ads-software.com/support/topic/api-not-working-10/

https://www.ads-software.com/support/topic/always-get-the-error-products-not-found-for-a-valid-product/