Using digital sign certificates for anaf.ro

Hi.
So in Romania there is this Drivere Token - Certdigital Semnatura electronica who offers a digital signature driver also for linux. The driver can be installed in Ubuntu mate 22.04.

anaf.ro requires this certificate for login.

From windows (of course) it works, but in ubuntu firefox, chromium and even edge browsers are failing to present the certificate to the website so I can login.

I called support from certdigital and they said that anaf.ro knows only how to query for the certificate in windows.

Found some discussions about it but with no end...(excluding virtual machine - I have dual boot anyway):

UPDATE

Done some digging intho their code and the js is calling

window.external.WebLogonNotifyUser()

UPDATE 2.
On e-guvernare.ro something similar is called:

window.external.WebLogonPassword

and the window.external does not have those values or functions on ubuntu....

And also seing edge comments in js code...