Let's call the upstream Wi-Fi provider JoesCornerCafe. Their AP would know, at a minimum, the MAC & hostname of the GL.iNet router. That's assuming it is as simple/dumb Wi-Fi hot spot as it gets.
On a cruise ship & more advanced networks that use captive portals/splash web pages before connecting (ie: MacDonalds), deep packet inspection (DPI) it is entirely possible to get info from the packets/HTTP/TLS headers flowing through any router right down to the size of web browser window you're using.
But they are able to know if you are behind another router, if they have rules against travel routers they make the ttl smaller so that devices with more than one hop gets blocked, but you can manipulate it.
The only other ways is when there is a misconfiguration, one very easy one is when you install avahi for chromecast routing but you forgot to deny interfaces for wan, the default configuration would leak multicast to the outside.
And ipv6 as non NAT that can be quite risky, since ipv6 has originally not a NAT implementation, it will either use the gua or the local ula prefix, there are many ways that can go wrong if not behind a NAT and when following the gua for local clients.