According to Higurashi Mei Bernkastel is the accumulated parts of Rika’s inhuman traits which she discarded.
And yes that includes the Hanyuu & Eua bits.
The portions of Eua made to drive Rika to St. Lucia are sent to Bernkastel as are the Fragments of Hanyuu ensuring that Rika keeps her Memories. End result: Bernkastel takes the form of Hanyuu to fight Eua at the end of Sotsu.
Unfortunately Black Witch Rika also is considered Inhuman Fragments of Rika so she gets shunted into Bernkastel as well.
Rika also starts using Role Cards which means that they get dumped into Bernkastel resulting in Bernkastel taking the forms of Kazuho and Nao.
I dare say the end of Part 3 of Higurashi Mei will reveal all this by traumatizing Nao to the point where she starts discarding the Nao persona which in turn reveals the Ayaka persona which discards herself due to the lack of Kazuho revealing the Miyabi persona who discards herself due to the lack of Aya revealing the Kazuho persona who discards herself due to the lack of Nao & Ayaka revealing an insane babbling Hanyuu-Rika Hybrid calling herself Frederica Bernkastel.
Rika will probably recognize Frederica Bernkastel and try to sort through her Fragments to find out what she can about her and wind up discovering what happened to the Hanyuu Fragments from Higurashi Gou as well as the fact that her urge to go to St. Lucia is artificially induced by Eua as well as the nature of Black Witch Rika.
Chances are the Black Witch Rika is the Kyrie of the True Rokkenjima Massacre so Rika’s priorities would be to get Bernkastel(now fully immersed in the personas of Hanyuu and St. Lucia Rika and now more capable of discarding unwanted taint) to head to the Ciconia Gameboard and grab the shards of Hanyuu & Chloe Ironside(the Rosa of the True Rokkenjima Massacre) and put them back together and seal the Black Witch away.
Of course this still doesn’t resolve the problem of the the Tsukuyami nor the mysterious writer rewriting Reality to his/her whims nor Une’s rampage.