Plugin checkState, combination and Kerberos

Trying to use checkstate plugin (https://lemonldap-ng.org/documentation/latest/checkstate.html) with a setup using combination Kerberos/LDAP

Using a bad username works (the check fails) but a valid username and a bad password works.

Logs just say authentication is valid:

[Thu Sep  9 17:25:08 2021] [LLNG:60228] [debug] Check configuration for Lemonldap::NG::Handler::PSGI::Main
[Thu Sep  9 17:25:08 2021] [LLNG:60228] [debug] Get configuration from cache without verification.
[Thu Sep  9 17:25:08 2021] [LLNG:60228] [debug] Lemonldap::NG::Handler::PSGI::Main: configuration is up to date
[Thu Sep  9 17:25:08 2021] [LLNG:60228] [info] No cookie found
[Thu Sep  9 17:25:08 2021] [LLNG:60228] [debug] Build URL https://auth.example.com/checkstate?secret=secret&user=coudot&password=test
[Thu Sep  9 17:25:08 2021] [LLNG:60228] [debug] Redirect 1.1.1.1 to portal (url was /checkstate?secret=secret&user=coudot&password=test)
[Thu Sep  9 17:25:08 2021] [LLNG:60228] [debug] User not authenticated, Try in use, cancel redirection
[Thu Sep  9 17:25:08 2021] [LLNG:60228] [debug] Start routing checkstate
[Thu Sep  9 17:25:08 2021] [LLNG:60228] [debug] Processing controlUrl
[Thu Sep  9 17:25:08 2021] [LLNG:60228] [debug] Processing code ref
[Thu Sep  9 17:25:08 2021] [LLNG:60228] [debug] Processing code ref
[Thu Sep  9 17:25:08 2021] [LLNG:60228] [debug] Launching ::Issuer::SAML::storeEnv
[Thu Sep  9 17:25:08 2021] [LLNG:60228] [debug] Processing getUser
[Thu Sep  9 17:25:08 2021] [LLNG:60228] [debug] Processing authenticate
[Thu Sep  9 17:25:08 2021] [LLNG:60228] [debug]  -> authResult = 0

But no Kerberos ticket is sent here.