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What you mean integrate on "all my APIs are in Azure App service and this has to integrate with Windows desktop application.". Try to explain a little bit what's your requirements.

If you want to Read/Write a SQL DB on premises, you can use a Azure Gateway without deploy anything in your server, another choice with SQL Server is to move the DB to Azure (if supported). You can use the triggers on Azure Functions to write/read something on Azure Storage, from your Server you can read the storage and perform some tasks. As you can see there are multiple choice without writing much code on premises, try to clarify your requirements.

A Pro of Azure Service Bus is reliability and persistence: you can send message when receiver is offline; receiver can read it when it back online. A Cons is costs and message size. You can consider also SignalR

I'm currently working with vue as 4 years now, I'm moved away from Angular 2 when it become a different framework, I gave Angular a try but personally I found vue much similar to angular first version. About Vue vs React you can read vue comparison with other frameworks. From wikipedia: Vue was created by Evan You after working for Google using AngularJS in a number of projects. He later summed up his thought process: "I figured, what if I could just extract the part that I really liked about Angular and build something really lightweight."

A PRO for VueJS is a very beautiful UI framework Vuetify and a CLI tools VueCLI.

As a CONS is the new release candidate version 3 planned for Q3 2020 witch introduce significantly changes.