At my company, we purchased a licence of Rstudio Connect to help our user deploy content, among them shiny apps. The product is really awesome and it worth the licence cost. This is ready-to-use as soon as the shiny apps is working locally - deployment is really easy!
For special apps, we also have an instance of shinyproxy, an open source solution based on docker deployement for shiny apps. As we use DevOps pratice at our firm, it helps on some project to deploy an apps based on Shiny. This solution is open source but needs some involvement on devops pratices and skills in docker for example.