RStudio will begin indexing a project immediately after RStudio is launched, so if the project indexer were the culprit, I would expect the slowness to manifest immediately after launching RStudio and perhaps subside after the project indexer has finished running.
It's interesting that the sum of user and system timings is typically less than elapsed timings for RStudio's case. I think this implies that RStudio is doing work behind the scenes that R is not capturing; the project indexer is one such thing that could be implicated here, but it could also be e.g. a long-running old completion request that inadvertently caused a listing of files in the filesystem.
Would you be willing to also provide a screenshot of the event log in the case where the R session is getting stuck? In particular, I'd like to see what the event log looks like immediately after the console prompt finally shows up.
As a side note, after showing the request log (with Ctrl + `), you can press e to get a JSON representation of the event log, which you could then share with us so we could see exactly what requests were being made to the R session. (You could copy the JSON to a file, and then upload it somewhere we could take a look.)