New Xcode installs usually need the command-line tools to be updated. Otherwise, Monterey didn’t break Git or Stan for me (I don’t use Docker).
I’d suggest moving to cmdstanr unless you need log density or gradients or transforms directly from R. It keeps up with the Stan releases and is easier to install than RStan.
CRAN version of RStan is 2.21. GitHub install version is 2.26. Stan itself is at 2.30, so they’re 2 and 1 years behind respectively. To install the latest RStan from GitHub, see: RStan Getting Started · stan-dev/rstan Wiki · GitHub.
The reason CRAN’s behind is that new CRAN policies on dependent packages have blocked our releases when combined with their aggressive downstream consistency checking.