The basic workflow at Gateway side is inspecting all HTTP port 80 traffic (with iptables or others), If the URL is about internet detection, reply a 301 redirect to the captive portal URL.

But the URL is too complex among different vendor:

https://captivebehavior.wballiance.com/

I don't know why, even I tracked the URLs, sometimes it still fails (OS refuse connecting to the URL?).

DHCP option 114 (RFC8908) can advertise the URL to client directly, but it is not widely supported:

https://developer.apple.com/news/?id=q78sq5rv