Should I include other domains in the property setup?

If you plan on adding integrated analytics tools and the site spans multiple domains, then it’s necessary to consider how DTM should treat traffic between domains. If user data persists across the domains, check the box indicating ‘This site spans multiple domains’ and list the applicable domains in the box that expands.

See help link https://marketing.adobe.com/resources/help/en_US/dtm/t_create_web_property.html

Note: If you do not intend to integrate an analytics tool, this step is unnecessary and does not affect processing.

The other benefit / effect of this setting is anything that is noted here becomes available as a rule criteria when using the built-in 'domain' criteria. So, you can tell a rule to fire on specific domains: