We had a similar problem in Sweden when trying to renew passports. A black market developed as covid eased. Everyone was trying at the same time. Some one made a browser extension which repeatedly tried to book appointments. The government implemented a governement ID system before making any bookings. The problem disappeared!

We still have a similar problem trying to get a driving test time. The driving schools book every slot for months ahead. They are commonly referred to as a mafia. You basically cannot get your license without paying a driving school a ton of money.