I installed rstudio-server on WSL2 in Windows 10. It starts fine and shows the login popup. It accepts my credentials but the login popup persists and requires repeated login (infinite loop). I tried to locate the logs to see the problem but I cannot find them (or perhaps they are not created?) Thanks for help on either the login or the logfile issues.
Perhaps the support article at Using RStudio Server in Windows WSL2 is helpful in some troubleshooting.
Also, refer to https://support.rstudio.com/hc/en-us/articles/200554766-RStudio-Server-Application-Logs for a discussion of the location of log files.
If none of this is helpful, please provide some more information, e.g. the result of rstudio-server status, your operating system, etc.