All the Connections tables are stored in the same database that WordPress was installed in. You need to use phpMyAdmin or similar tool to do an sql export of all the Connections tables. They are easy to identify as they all have “connections” in the name. Once you have exported the sql file, you can import that sql file into the new database. If the Connections tables already exist in the new database, you will have to drop/delete them before you import. It sounds like a lot but it only takes a few minutes with most of the time spent on logging in and out.