I think where to go to broaden your programming skills depends also on what you want to do.
If you manipulate lots of data stored in database, SQL is a very good choice. Yes dplyr ease a lot the work with DB but it is nice to have so skills to go further and know what could be done in DB. It is useful outside of the R world too to play with data.
I second the recommendation on C++ very useful if you need to improve some performance or use R as a friendly DSL around some C++ library that could be of any use to you.
As datascientist, I find useful to have some skills and understanding in Python if you want to use machine learning models as Keras or tensorflow. Even if RStudio made easy the use of python through with reticulate and used it to offer [Keras}(https://tensorflow.rstudio.com/keras/) and tensorflow model to the R community.
Also, if you want to develop your skill in the publication part with dynamic Rmarkdown report or some shiny apps, CSS, HTML could be useful, and a little JavaScript. It allows you to customise what you are doing and go further in some corner cases.
These are the language I am looking to in complement with R to go further in some situations where I found myself limited.