The magical captive portal thing you get doesn’t show up on all captive portals.
And of course it should not be broken, but we have an old browser and they probably did something really silly on the web page.
It should just work™, but when it doesn’t these are normal things you can do.
Your silver bullet is flypig doing the browser/webview uplift.
And if you keep reading you find that the whole point of the page is to be susceptible to what is effectively DNS spoofing to shove the login page in your face. (And other similar debugging uses).
You are not really meant to interact with neverssl itself, and it’s not like it is your bank anyway… some publicly available text going unencrypted never hurt anyone.
But you are! They are just not routing your traffic to the actual internet yet.