Detecting captive portals re-establishing is a separate, but linked issue. It's mostly solved too.
Setting aside a VPN client, your browser and/or OS will send out a http get request to a site which returns "OK" or "success". If it returns a redirection, then it will go "ahha I'm behind a captive portal" and pop up a page for you to log in.
VPNs do something similar. The MozillaVPN client for example will periodically check for reauthentication by doing a http call over the non-VPN route to a server and looking for a response saying "success". If it needs a redirect it flags up a message on the client to disable your client and reroute traffic via normal networking to allow reauthenticaiton.
What I want from a wireguard client is it to check for captive portals outside (in a situation I'm routing the entire of 0.0/0 via wireguard), but also check for reachability inside the tunnel. Have "check" and "checktime" parameters, which poll a given server (presumably via the tunnel) preset a popup to reauthenticate.