Hi Rodney,
I don't have fist-hand experience with RabbitMQ, but their tutorials show example for C#/.NET Core https://www.rabbitmq.com/getstarted.html and they provide a .NET Core client https://www.rabbitmq.com/dotnet.html Therefore, this should work fine with PowerBuilder 2019's C# Web API projects.
If you want to stay with client/server architecture instead of n-tier/cloud architecture, then theoretically you could integrate RabbitMQ by creating a COM wrapper for their C/C++ clients and integrating that int your client app. Here is an open-source C language client: https://github.com/alanxz/rabbitmq-c
However, if you go with a message broker like RabbitMQ, I think architecturally speaking it makes more sense to do this with C# Web API project of PowerBuilder 2019 so more business logic is on the server side. You would then invoke the C# Web API you have created with PowerBuilder from your PowerScript app using the new RESTClient or HTTPClient objects.
As far as alternatives to RabbitMQ, I would recommend doing some Google research. One thing to note is that there are newer generation message brokers than RabbitMQ, and these days Amazon, Azure, etc. all provide their own implementations as well. Here is an article I found that may be useful to you: https://www.upsolver.com/blog/kafka-versus-rabbitmq-architecture-performance-use-case
Regards,
Armeen