Custom Domains Clarification

Looking for some clarification on custom domains.

I have a domain lets call it my-domain. From here, I have various applications deployed across many sub-domains of this domain. For example, an application in a staging environment might be found at staging.my-domain.com and other applications in staging may be at dashboard.staging.my-domain.com. I’ve configured my Auth0 Custom Domain as auth.staging.my-domain.com ( per the docs on custom domains). Will this enable the required cookies to be used across all subdomains of staging.my-domain.com? Furthermore, I’d like to double check that these same cookies would not be able to be used in the non-staging subdomains, i.e. app.my-domain.com (Without staging. subdomain).

More generally, is the cookie acquired from auth.staging.my-domain.com valid for *.staging.my-domain.com and invalid for *.my-domain.com otherwise? Am I thinking about this wrong?