Add-TtmSiteTypeKey does not configure a Publication to be a Site Type (you do that by setting the Publication's Publication Type to "Site Type"), but it associates a Site Type (Publication), with Web Application(s) in Topology Manager.
This is done to be able to infer Publication Mappings from the Site Type (if you use the Site Wizard).
The "Site Type Key" (i.e. the Key of the Publication/Repository acting as Site Type) is stored as
ScopedRepositoryKeys property on several entities in Topology Manager: WebApplication, Website, CdEnvironment, CdTopology.
This mechanism is not intended to be extensible, but Topology Manager does provide an
ExtensionProperties property on all entities, which is intended as general purpose extension point; it allows you to add key/value pairs to each entity.
ExtensionProperties on WebApplication and Mapping entities are also pushed to Discovery Service (which also has such extension properties).