Deployment of applications is not limited to Shiny Apps. What you need is to create a bash file called app.sh  in your work directory. Inside this script you define the steps of deploying your application. For instance for a Bokeh app inside myapp.py , you can enter bokeh serve myapp.py 

Then from the magic corner, select, App Settings and enter the deployment port following letter p, and then enter the application link, if any. For instance, if your application serves at port 5006 and it runs on myapp link, you should enter like this example:

And the result of your app is:

It's an equivalent of http://localhost:5006/myapp .
Similar to Shiny Apps, you can see the log file, in Files in your Application page:
 

You can also generate specific log files or outputs and drop them in the shared folder to track or share with someone else. 

For APIs, you can follow the same process where you define the structure of your API inside your application codes and app.sh  start script.

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