I was able to get InstallR to execute on Mathematica 14.0 and link to R 4.1.1 (curiously, I could not get it to interface with a more recent version of R).

However, when I attempt to execute REvaluate, I get the error messages e.g. Error: package 'methods' could not be loaded

Even though library/methods and the other packages that REvaluate throws the error for are installed and can be loaded while in R. The details of the error are rather generic, but perhaps someone has encountered a similar problem and knows how to fix it, i.e. I load to libraries that have other libraries such as methods as dependencies,

REvaluate["{library(glmnet);library(MASS)}"]

and the resulting error is:

Error: package or namespace load failed for ‘methods’ in dyn.load(file, DLLpath = DLLpath, ...):unable to load shared object '/opt/R-4.1.1/library/methods/libs/methods.so':/opt/R-4.1.1/library/methods/libs/methods.so: undefined symbol: Rf_allocS4Object Error: package ‘methods’ could not be loaded*

as noted, libs/methods/ does exist. I assume that methods.so is a file that is being created to link to the library, which suggests that something fails when Mathematica attempts to do so.