How can I restore deleted system cache in `/BuildRoot/Library/Caches`?
Let’s assume your Mac can boot and run Safari.
Go here, and download Sierra and reinstall on top - that drops a functioning system on top of your accounts, files, apps.

https://support.apple.com/en-us/HT211683

Assuming that didn’t work, we would need to understand the rsync command in detail and perhaps troubleshoot that, but since rsync comes with macOS - you likely have that from the system.