I'm having the same issue. I recently updated R, RStudio, and RTools.
I've uninstalled all versions of each of these and reinstalled them after restarting my machine.
I also tried turning off Windows Firewall and adding RStudio to the exemption list.
I'm using Windows 10. R-4.0.5. RStudio 1.4.1106. Getting exactly the same message when I open RStudio.
I've been stuck on this all day - can't install any packages ...
UPDATE: I reinstalled R with both x64 and x32 versions, then ran RStudio using the R x32 version (hold Ctrl while opening RStudio and select x32 version). This worked for me - I'm back up.