7.8.2003 Upgrade works but UI still says 7.7.1908

As @giacomo said, the file is /etc/os-releasein particular the key VERSION. If you try to check the content of that key you should see the correct system version.

If you try to change it, save the file and execute systemctl restart cockpit then Ctrl+Shift+R to hard refresh the cockpit login page, you should see the same version.

Have you try it?

PS. that file is a NethServer template: /etc/e-smith/templates/etc/os-release/10base