I had this same issue. I think there is a problem with the Big Sur update to the R package (arm64 package). I removed all R and R studio files from the applications folder and emptied the trash. Then I downloaded the prior version (High Sierra and above, 4.1.0) from the cran repository (R for macOS), installed it and then tried to reinstall the R Studio download. It opened up fine.
Not sure what Arm64 is, but R Studio wasn't a fan. Hope it works for you!