If you don't mind clarifying a bit more about the approach you went through? Are you aware of RStudio Connect's new feature to "watch" a GitHub repository, essentially making Jenkins unnecessary?
It is talked about more here:
https://blog.rstudio.com/2019/06/24/rstudio-connect-1-7-6/
That said, CI deployment (or git-backed deployment) of Plumber APIs is very much the same on RStudio Connect.
- create content endpoint
- build manifest
- upload
- deploy
The manifest / bundle upload is what determines whether the content is a Plumber API or Shiny App.
This article explains in more detail:
https://solutions.rstudio.com/deploy/overview/
If you have more specific questions or details around what you did, we would be happy to help clarify!