A RStudio Connect is definitevely a product you can use on premise to publish Rmarkdown production but also shiny apps and API service (thanks to plumber ). Then you could publish links to your R production in you confluence wiki.
About Rmarkdown, it is a format that allows to mix text edition using Markdown syntax with code chunks, mainly in R but also in other language. Rmarkdown allows then to convert Rmd files in md files where all code chunks have been executed, code and results wrote in the mardown file and plots or others artifacts available to the markdown file. Then pandoc is used to produce output format like HTML files.
I wanted to precise all that because I don't know which formats you can publish to Confluence. If you can publish HTML files, seems to be no problem. If you can publish markdown files in confluence, I think it could be possible to.
In general, when you'll know which formats is better for publishing environment, either it is already available or you will have to build your custom output format.
For confluence, know that you won't be able to publish interactive html document with shiny embedded. Just "static website" as HTML with htmlwidgets.
Hope It helps in someone way.
I never experience this kind of publishing so can't be more precise about confluence. We have one at work but we also have a RStudio Connect server for all our R work. So we use it for publishing.