Update: I created a new package to help pre-compile CmdStan models in R packages:
instantiatepackage: Pre-Compiled CmdStan Models in R Packages • instantiate- Announcement: {instantiate}: pre-compiled CmdStan models in R packages
The models compile at install time, but they skip compilation whenever CmdStan or cmdstanr is not found, which will make it possible to submit to CRAN.