rsync is a different program than ssh, installed as a different package, so it does not matter what license it has. In most cases, ssh will run a bash at the remote end, which also has the GPL license, so it should be obvious that it is irrelevant what license have the programs launched by ssh.
When you run rsync over ssh, the local rsync starts the local ssh client, which connects to the ssh server, which runs the remote rsync, while the data is piped through the ssh connection.
rsync is available for most operating systems, but it is not usually installed by default. OpenBSD might be the only exception without a rsync package, but it has openrsync. I assume that it uses the same protocol so rsync to/from OpenBSD should work as well as to/from Linux, Windows, MacOS or any *BSD.
If you have the right to transfer files to a computer then normally it is very simple to install rsync, only for your own user if do not have admin rights.
In most cases, you can initially just copy the rsync executable file to the target computer using scp, and then do any other file transfers with rsync over ssh.
After I have abandoned both scp and sftp many years ago, I no longer had any problems with the performance or data integrity of file transfers over ssh.