appleid 502 Gateway Message

Is macOS or Windows running on that desktop? Your footer implies Windows.

Checked for updates, and tried rebooting the desktop recently?

Checked for updates for iTunes too, if running Windows.

If this is your network, maybe also reboot the router?

Any add-on VPN apps, add-on anti-malware apps, add-on cleaner apps, or other such?

Try the above suggestions, and then also remove add-on anti-malware, restart, and try the access again.