This is an institutional decision of the organisation where the supervisor is meant to be recruited by the time the project starts: if it is possible for them to have somebody not employed acting as staff in a European project.
If the answer is yes, then the applicant should go ahead with that institution, they can include the information on the institution’s infrastructure and capacities.
If the answer is no, then the applicant should include information on the institution where the supervisor is recruited at present. In that case, if a change of host has to be asked for, it should happen at GAP stage.
Having in mind that the supervisor is the official contact for the beneficiary in the project proposal, another solution is that the applicant includes someone else as the main contact/ supervisor, for example head of the lab/ institute, and list the other one as co-supervisor. From the point of view of a reviewer, the fact that the actual supervisor is not yet employed by the organisation is a potential risk. It would make the proposal stronger, if the employment contract were already signed (with a future start date), or there would be something else in place to ensure that the person is employed by the start date of the project at the latest.