When you create a ServiceBusClient instance and use it to send messages to a topic, it will open a single-brokered connection that it uses for all operations. This connection stays open for as long as the ServiceBusClient instance is alive, and it's used for all operations that you perform using this client, including sending messages to multiple topics. Therefore, if you have a singleton ServiceBusClient that you're using to send messages to multiple topics, this would typically count as a single brokered connection, provided that all these operations are happening concurrently in the same process. In a nutshell, the number of brokered connections is generally equivalent to the number of ServiceBusClient instances that are actively communicating with the Service Bus service.
So, while a singleton ServiceBusClient within a single process would generally count as a single brokered connection, the actual number of brokered connections can vary depending on the specifics of your application and how it interacts with the Service Bus service.