Installation of the Open Source RStudio Server is done under your own responsibility indeed. For the professional products, e.g. RStudio Workbench, additional options exist to support installation and with regards to functionality, however.
With the pro-products you would gain access to the RSW Launcher amongst many other features. With the Launcher you can automatically launch your R session either locally or remotely on a SLURM based HPC compute node or on a Kubernetes cluster out-of-the-box.
I am not aware of any restriction for using your "CLOUD - Wide" R with Rstudio Server. You simply need to make it available on the RStudio Server and ensure that it still works (e.g. if mounting the R installation tree via NFS, you need to make sure that all OS dependencies are met on the RStudio server). If you can be more specific on how you want to use your "CLOUD - Wide" R, I'd be happy to discuss more.
If using OS RStudio Server you still can utilise various R packages that support remote submission to a HPC cluster. One of the more elegant and performant versions I have come across is the
clustermq package. With a bit of tweaking you could use a passwordless ssh connection from your RStudio Server to the HPC and from there you could automatically get the jobs submitted to the HPC cluster, all via a concatenation of
clustermq's ssh connector and the SLURM/LSF/... template (with
clustermq you would not even be limited to have a SLURM cluster as it supports quite a few schedulers. Once set up you only could use the
Q() function and the code chunk encapsulated in this function call will be remote executed.