Mentioned article is using an SDK written and maintained by WEBCON, so the integration with Autenti is pretty easy as it's just installing ready package.
It's source code is here: https://github.com/WEBCON-BPS/BPSExt-Signing-Autenti
Also i've found that Autenti can sign documents with mSzafir: https://autenti.com/pl/blog/jednorazowy-certyfikat-kwalifikowany-mszafir-dostepny-na-platformie-autenti
Not sure if there is ready SDK to integrate with Szafir, but looking at their website there is possibility to get .NET compatible developer packages here:
https://www.elektronicznypodpis.pl/oferta/narzedzia-programistyczne/
Prices here: https://www.elektronicznypodpis.pl/oferta/cennik/
Seems like there are 2 possibilities - using Autenti, or developing custom tooling.