Actually I believe that Katherine and Stefan are suppose to be together.
Why?
Stefan's personality is not simular to Silas and Amara from inference from Silas and Tessa is more like Elena than Katherine. So Stefan doppelganger should be a shadowself Amara. Elena is a doppelganger of Amara but she is not a shadowself of Amara. Katherine is a shadowself of Amara,
Shadowselves personalities are more different than the previous selves. i.e. Amara=good, unknown doppelganger=bad, Tatia=good, Katherine=bad, Elena=good.
Silas=bad, Stefan=good.
A good doppelganger (Stefan) connects with a bad doppelganger (Katherine).Â