cellman, yes, that's exactly the purpose of cloud.microsoft being a dedicated, yet common eTLD+1 domain root for Microsoft SaaS products. Products under cloud.microsoft have an option to securely share data/authentication/cookies across *.cloud.microsoft domain hierarchy and browsers support it as the 'same site' requests. This means that as the user navigates across different web applications under *.cloud.microsoft domain, the context established with one app can be shared more seamlessly for the benefit of better user experiences (e.g. less redirects and duplicate sign-in prompts). This will become even more important as browsers plan to restrict cookie sharing across different eTLD+1s, where domain1.com vs domain2.com (and similarly subdomain1.microsoft vs. subdomain2.microsoft) will be treated as 3rd party to each other and app experiences spanning them will get a bit bumpier.
There are many other benefits of having a common eTLD+1 cloud.microsoft domain root, dedicated for SaaS products and services. Many domain related security, trust, compliance settings cascade from this level down the DNS hierarchy, benefiting all applications and services underneath it, which means more secure and trusted experiences with those apps for users and customers.
Obviously sharing a common eTLD+1 root between apps and services means that we have to keep a very high bar on what is and is not allowed in. For more information see Unified cloud.microsoft domain for Microsoft 365 apps | Microsoft Learn