Let's think on this scenario (all hits are send to same Report Suite):
What does it will happen with visits? Are we going to have on this case 1 visit or 2 visits (1 for each domain)?
I assume you are using the Experience Cloud Id, and all sites are pointed at your organization (this will mean the user cookies should identify the same user). Then you should just make sure all the domains are configured as "Internal Servers", it should track as a single visit... you don't want to link out to the second domain to trigger an exit link.. that causes some issues (but if all servers are set as internal this shouldn't happen).
I use a global suite setup that has multiple domains on it, and when moving from site to to site they are treated as part of the same visit.
The Experience Cloud ID Service cross domain works if the 3rd party cookies are enabled. As you know 3rd party are less and less used, so please bear in mind.
Another approach is to pass the visitorID across the domains with this method: