Using cookies to authenticate with micro services

I have a service stack api that is working great with authentication using cookies. We want to add a second service and use the cookies issued by the first to authenticate against the second. We have a typescript frontend and it doesn’t send the cookies when making requests against the second api. Is there any way we can make this work or is it simply not possible?

Cookies are tied to a domain so each site would need to be hosted under the same domain for browsers to include the same cookies in HTTP Requests to each site.

This can be done using a reverse proxy where multiple internal sites are hosted under the same external domain, e.g: