Set-Cookie on header yet Cookie is not being set

I have a NestJS Application server being hit from an Angular Webapp. My NestJS server is located at https://api.example.com while my Angular app is hosted at https://example.com

I sent the {withCredentials: true} option on my Angular HTTP Post to login, and the response comes with a Set-Cookie header as follows:

SessionId=XXXXXXXX; Path=/; HttpOnly=false; Secure; Max-Age=3600;

Since the Set-Cookie header is passed successfully from the server --> frontend, shouldn't it be set? I programmatically try to access the cookie in subsequent requests and it's always null.

Thanks!