For many purposes, e.g. content translation, we expect a user session to span multiple projects. Currently, we prefix all cookies by the dbname and its domain is defaulted to the current domain.
To have a cookie used on all subdomains, we would need to specify overrides for these defaults when storing the ID using mw.cookie.
In addition to the current wiki-specific session ID ("mwuser-sessionId"), we should have a cross-subdomain session ID (e.g. "xsd-sessionId", idk) that can be used in cases like Content Translation analytics.