(Reopening this topic as it came to me through a support channel, and I think the answer is important for people to know)
By default, renv creates project libraries that cannot be moved to a different machine or even user account, due to its reliance on a global cache that sits outside of the project directory. This is exactly the behavior that you want if you're doing local development, but it is problematic for your scenario.
Fortunately, renv includes a solution for this problem. On the development machine, inside the project, call renv::isolate() and this will remove the reliance on the cache. You should then copy the entire project directory, including the project-specific .Rprofile, to the server.
Hope that helps.