From the download website, it seems RStudio support Debian 12. I have installed R 4.3.2
R version 4.3.2 (2023-10-31) -- "Eye Holes"
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On Mint (and presumably Ubuntu -- not sure about Debian) there should be a symlink /usr/lib/libR.so pointing to /usr/lib/R/lib/libR.so. Do you have both of those, and do they both have read permissions for non-root users?
There are multiple messages in the community about that error message, but the ones I found all seem to involve RStudio Server rather than the RStudio IDE.
I don't use RStudio Server (and I'm on Mint, not Debian), so I'm guessing here. If you have (had) RStudio Server installed and you use apt, you could try sudo apt purge <package> where is the package name you would use if you were installing it with apt get. Other than that, the best I can suggest is to try running RStudio from a terminal with rstudio --run-diagnostics. It will write some progress reports and possibly error messages in the terminal, and also will create a text file with a lot of information (and print the location of the text file in the terminal). Possibly something in the terminal output will be helpful. I get a number of error messages when I do this even though RStudio opens successfully, so you will need to wade through the output. Possibly it will print something more informative than the error message you have already gotten (but maybe not).
[108945:1205/121505.768076:ERROR:gl_factory.cc(120)] Requested GL implementation (gl=none,angle=none) not found in allowed implementations: [(gl=egl-angle,angle=default),(gl=egl-gles2,angle=none)].
[108945:1205/121505.770069:ERROR:viz_main_impl.cc(186)] Exiting GPU process due to errors during initialization
Attempting to launch R session...
. R_HOME = /usr/local/lib/R
. R_DOC_DIR = /usr/local/lib/R/doc
. R_INCLUDE_DIR = /usr/local/lib/R/include
. R_SHARE_DIR = /usr/local/lib/R/share
. LD_LIBRARY_PATH = /usr/local/lib/R/lib:/usr/local/lib:/usr/lib/jvm/jdk-21-oracle-x64/lib/server
. PATH = /home/zhenyu/.local/bin:/usr/local/texlive/2023/bin/x86_64-linux:/usr/local/bin:/usr/bin:/bin:/usr/local/games:/usr/games
. HOME = /home/zhenyu
R session launched, attempting to connect on port 36171...
TTY detected. Printing informational message about logging configuration. Logging configuration loaded from '/etc/rstudio/logging.conf'. Logging to '/home/zhenyu/.local/share/rstudio/log/rsession-zhenyu.log'.
unable to initialize the JIT
2023-12-05T04:15:05.986986Z [rsession-zhenyu] ERROR R SUICIDE: unable to initialize the JIT; LOGGED FROM: void {anonymous}::rSuicide(const string&) src/cpp/session/SessionMain.cpp:1245
2023-12-05T04:15:05.986986Z [rsession-zhenyu] ERROR R SUICIDE: unable to initialize the JIT; LOGGED FROM: void {anonymous}::rSuicide(const string&) src/cpp/session/SessionMain.cpp:1245
Connected to R session, attempting to initialize...
[109011:1205/121506.044033:ERROR:gl_factory.cc(120)] Requested GL implementation (gl=none,angle=none) not found in allowed implementations: [(gl=egl-angle,angle=default),(gl=egl-gles2,angle=none)].
[109011:1205/121506.046541:ERROR:viz_main_impl.cc(186)] Exiting GPU process due to errors during initialization
I get the same "GL" error messages at start and end. They seem to be harmless. The only thing I do not get is the JIT message. There are multiple posts here about the same error message, almost none of which contain a solution. You might take a look at RStudio error starting R - #5 by JohnHCarsonJr (different OS) which contains a solution involving reinstalling graphics drivers. Sorry I can't be more help.