Do Logic Apps have some sort of built in geo-replication like the Azure Scheduler or Key Vaults? I can't seem to find any information about it.
I have seen some implementations using API management but that is for Logic App that use HTTP triggers, in my case I'm using Service Bus triggers.
If there is no geo-replication how would a disaster recovery implementation look like for my scenario?
I think you are asking three questions - How do I get a geo-redundant Logic Apps deployment and How do I get a geo-redundant Service Bus Messaging deployment and how do I use them in combination.
I would start with the Service Bus Messaging side as it is the foundation for the LA process. In order to have a geo-redundant Service Bus Messaging queue you have to use the Premium SKU and this article goes into detail on how it works: https://docs.microsoft.com/en-us/azure/service-bus-messaging/service-bus-geo-dr
For the Logic Apps side you would setup an LA in each region (primary and secondary) and point the Logic Apps to the alias for Service Bus Queue. You would then disable the Logic App in the secondary region and only enable it when the primary region's Logic App was not operational. This would have to be done with some endpoint monitoring scripting and then switch over to the secondary and disable the primary.
Like you said, there are other more automated options (Traffic Manager) when Logic Apps is being triggered by HTTP traffic but since you are reading queues the recovery is more complex.
