Interoperable Chat and Profile apps

Yes it is. That is the link a solid app will get after you log in. Most log ins allow to pass just the pod URL https://naturzukunft.solid.community to simplify the login process, but nevertheless https://naturzukunft.solid.community/profile/card#me is what the app will get. A WebID usually identifies a resource of type foaf:Person (or to be less academic “a person”).

So, if I understand you correctly you want to manager organizations and associate persons with it. This could be done by creating an organization resource (e.g. a foaf:Organization or vcard:Organziation) and link to the WebIDs of the persons that are member or partner of that organization.

I already experimented with forming groups in my group app.

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