Function shared_rooms_check 

async fn shared_rooms_check<T>(
    services: &Services,
    body: &Args<T>,
    user_id: &UserId,
) -> Result
where
    T: Sync,

Refuses a profile read withheld by limit_profile_requests_to_users_who_share_rooms.

Appservices and a user reading their own profile are exempt. The refusal precedes the existence check, so it discloses nothing about the profile.