RStudio Desktop fails to start up after the latest version of RStudio is installed on Macbook pro

That version of RStudio requires macOS 10.15 or higher. You can install up to macOS 11 (Big Sur) on the 2014 MacBook Pro. If you want to stay with your current OS, similar problems were reported using 2022.02 on macOS 10.14, but RStudio-2021.09.2-382.dmg worked while 2021.09.3.385 did not. See