If you do need to passthrough your mydomain.com cookies to a thirdparty.com domain, you can technically already do that now by implementing it as an endpoint and calling fetch('/my-endpoint')

I've been thinking more about how to best do this. The preferred way might be to use the same domain and have an application load balancer like nginx split traffic on the URL path (e.g. /api). This is for two reasons. Firstly, you might not necessarily want to cookie the primary/apex domain and have the cookie shared across all subdomains. You also might not want to do CORS because preflight requests add latency and CORS adds complication.

Cross-Domain Cookie Library This library is intended for cases where you have scripts running on different domains (i.e. domain-a.com, domain-b.com) that need to be able to set/share a cookie value across those domains. A few example use cases would be a third-party script that wants to set/share a user identifier across both domains, or a company that wants to track if a user signed up for a newsletter across both their main website and blog that resides on a different TLD. This library also offers a way of writing data to a cookie from a third-party script