renv uses junction points on Windows, to create "links" from the project library to the cache when possible, and the project library is normally located within the project's renv/library folder. Unfortunately, this doesn't work across different drives -- in these cases, renv will copy (rather than link) from the global cache.
One way to fix this would be to use a custom library path for your project on the shared drive; e.g. in your .Renviron:
RENV_PATHS_LIBRARY = <path>
where <path> is some suitable path located on your shared network drive.