@casino You’ll lose connection to the router when the router reboots. Normally, your PC will automatically reconnect to the router when the router finishes rebooting. And your browser will go back to the log in page after that.
If your PC does not automatically reconnect, then you need to manually reconnect. And, if after reconnecting to the router the browser page does not refresh, you can refresh the page manually (usually, press F5 with browser active).
Basically, if you are able to reconnect to the router after you initiate restore backup, it already finished restoring.