The proposed subsets other than associated require common ownership, and the associated set could have common ownership.
A '.well-known' file has been proposed as a machine-readable declaration of a sets membership, with an 'owner' property pointing to a "parent" domain name. European data protection law covers this concept within the definition of "controller" (Robert pointed this out in the last meeting 08-17-2022).
If the .well-known file also had a controller property containing an array of text string identifying the common owning pr controlling entity or entities, this would support automated checks for the validity of a set, leveraging the potential legal significance and possibilities for enforcement.
The 'controller' text strings could also be relayed to the user inside Storage Access prompts helping ito inform the user and increasing transparency.

‘controller’ means the natural or legal person, public authority, agency or other body which, alone or jointly with others, determines the purposes and means of the processing of personal data; where the purposes and means of such processing are determined by Union or Member State law, the controller or the specific criteria for its nomination may be provided for by Union or Member State law;