Cookie Domain - Tracking separate site subdomain

I have two sites:
1] www.mysite.com
2] subdomain.mysite.com
ssGTM] track.mysite.com

I need to track www.mysite.com as a completely independent site and see hits from subdomain.mysite.com as refferal

The cookies set by GA4 and GoogleAds must only apply to the domain www.mysite.com (and any sublevels: test1.www.mysite.com)

Cookies should be managed by the server.
Currently in the GA4di ssGTM client I have the setting active:
“Migrate from JavaScript Managed Client-ID”

How should I set the cookie domain and flag?
1] for clientGTM GA4 setting tag?
2] for ssGTM “GA4 Client”?
3] for ssGTM “Linker Conversions”?
4] In the GA4 Admin panel, how should I configure the domains at the “Data Stream” level (Include only domains…)

Thank you