Rsync is the correct solution. It does exactly what you want and nothing more. A script that uses rsync is future-proof. Other backup solutions depend on the maintenance of the software, which could be abandoned, go up in price, or have vulnerabilities.
It didn’t used to be this way. You used to apply for copyright like a patent. Rich people stole content from poor artists that didn’t have the lawyers to file copyright. This broken system has been reformed. Nowadays, if you create something, you automatically own the copyright. You now have to “opt out” of copyright with an explicit license to “release” the rights. Much better system.