This C# code seems to have worked.

private static Output<string> InitializeCommunicationsServices(Output<string> rgSharedName)
{
	var communicationService = new CommunicationService("commsvcs-shared", new CommunicationServiceArgs
	{
		CommunicationServiceName = "commsvcs-shared",
		DataLocation = "United States",
		Location = "global",
		ResourceGroupName = rgSharedName,
	});

	var keysResult = ListCommunicationServiceKeys.Invoke(new ListCommunicationServiceKeysInvokeArgs
	{
		CommunicationServiceName = communicationService.Name,
		ResourceGroupName = rgSharedName
	});

	return keysResult.Apply(k => k.PrimaryConnectionString)!;
}

I haven't gotten as far as using the

Azure.Communications.Sms

nuget package to interact with the service yet, but what I see in the Azure portal looks good.

One more thing, again, in case anyone ever follows along or cares... Creating the Azure Communications Services resource via Pulumi took 97 seconds. Slowest resource creation I've yet encountered.