How to register ServiceBusClient for dependency injection?

ServiceBusClientBuilderExtensions.AddServiceBusClient is an extension method of IAzureClientFactoryBuilder:

public static IAzureClientBuilder<ServiceBusClient, ServiceBusClientOptions> AddServiceBusClient<TBuilder>(this TBuilder builder, string connectionString)
            where TBuilder : IAzureClientFactoryBuilder

To get an instance of IAzureClientFactoryBuilder, you need to call AzureClientServiceCollectionExtensions.AddAzureClients(IServiceCollection, Action<AzureClientFactoryBuilder>) for a given IServiceCollection, which provides a delegate giving an instance of IAzureClientFactoryBuilder. (this method is in the Microsoft.Extensions.Azure NuGet package)

To call that method, you can use the IServiceCollection provided by IFunctionsHostBuilder. With all of that, what you have should look something like:

public override void Configure(IFunctionsHostBuilder builder)
{
    builder.Services.AddAzureClients(clientsBuilder =>
    {
        clientsBuilder.AddServiceBusClient(Typsy.Domain.Configuration.Settings.Instance().Connections.ServiceBusPrimary)
          // (Optional) Provide name for instance to retrieve by with DI
          .WithName("Client1Name")
          // (Optional) Override ServiceBusClientOptions (e.g. change retry settings)
          .ConfigureOptions(options =>
          {
              options.RetryOptions.Delay = TimeSpan.FromMilliseconds(50);
              options.RetryOptions.MaxDelay = TimeSpan.FromSeconds(5);
              options.RetryOptions.MaxRetries = 3;
          });
    });
}

To retrieve the named instance, instead of using ServiceBusClient as the injected type you use IAzureClientFactory<ServiceBusClient>. The ServiceBusClient is a Singleton regardless of whether you use a named instance or not.

 public Constructor(IAzureClientFactory<ServiceBusClient> serviceBusClientFactory)
 {
     // Wherever you need the ServiceBusClient
     ServiceBusClient singletonClient1 = serviceBusClientFactory.CreateClient("Client1Name")
 }