Synchronize 2 x Database, MySQL/WordPress and firebird

It is necessary to synchronize 2 x DB, the php/MySQL/WordPress/firebird stack. There is a medical clinic. They have a server that stores all the data - doctors, clients, schedule, appointments. All this lies in the firebird database, to which you can connect remotely. There is a site on wordpress of this clinic. There is a time booking plugin, i.e. appointments. It is necessary to synchronize the database of the wordpress site and the firebird database. It is necessary that the information that goes directly to their firebird database, i.e. the manager, for example, created a new appointment for an appointment, a new client, so that this data enters the wordpress database. This is so that you can see on the site what time is occupied, how free, what doctors there are. And vice versa. An order was received from the site, this information should go to the firebird database on the server, so that there is also up-to-date information. Actually, it seems that the task is to understand how this booking plugin on wordpress works, what tables it uses, how it stores data there in order to actually exchange this data with the firebird database.