Hello! I'm sorry to hear you're having issues with storage space, I can try to help you with this.
There are a few places I can think of where those old game files may be. Here we go -
- C:\Program Files (x86)\Ubisoft\Ubisoft Game Launcher\cache\download\
- C:\Program Files (x86)\Ubisoft\Ubisoft Game Launcher\games\Tom Clancy's Rainbow Six Siege\
- C:\Program Files (x86)\Ubisoft\Ubisoft Game Launcher\games\Tom Clancy's Rainbow Six Siege\download\cache\
Try to check the size of these folders to see if they're larger than expected. The cache folders are usually empty or small, and the Rainbow Six Siege folder should be the size of one installation.
I hope that helps you