There is a difference between Rika, Frederica Bernkastel and the witch Bernkastel. Now it's entirely possible that the last two are one and the same. But even if they are, I think it's fair to say that you can still treat Frederica Bernkastel (having only lived a 100 years) and the witch Bernkastel to be two different entities. Any authoritative sources further clarifying their relation would be nice.
Throughout the events of Higurashi, Rika and Frederica Bernkastel are more or less the same. In Saikoroshi we get a clear point where Rika lets go of the Frederica Bernkastel part and clearly states that she might continue to exist on a higher plane. It's worth noting that at that time, Rika (and thus Frederica) refers to herself as a witch.
Now what we can gather from Umineko regarding Bernkastel's origin is that she
wasn't a witch, but instead a game piece. Not even self-aware according to Lambdadelta.
The game board was constructed by her master, furthermore
due to a logic error, the game was broken with no goal at all. Ultimately Bernkastel managed to escape through a miracle and gained the status as the Witch of Miracles.
Now, it's fun to theorize that this is all (directly) linked to Higurashi. Especially if you also consider Featherine, the "evidence" just seem to pile up. Bernkastel being the miko of Featherine translates nicely to Rika being the miko of Hanyuu, for example. The manga of Umineko provides even further clues, implying that Hanyuu was most likely Bernkastel's master. The time spent by Bernkastel in this logic error is supposed to be centuries.
But there are also significant problems with this comparison. First of, it's unclear if this game was crafted by anyone to begin with. From our perspective it came to be when the strong will of Takano clashed with Hanyuu saving Rika by going back in time (or rather, to another fragment). If this quantifies as setting up the game, than Hanyuu would indeed be the game master. Lambdadelta's wording implied some ill will and indicated that the game master lost sight of the goal partway through, but from the get go Hanyuu seems to want to find a world where Rika and her friends can live peacefully.
Second of all, where would the logic error be? The inability to escape was mostly down to missing crucial information. Rika/Frederica Bernkastel was able to determine rules XYZ but unable to workaround them. In the end they did call upon some miracles in their final battle, but really this wasn't like the infinite monkey theorem at all. Last few arcs we see Rika gain significant insight in how to avoid tragedy and combining all effort and hope in a final battle. This is also apparent in the second episode of Gou, as Rika states quite confidently that she'll be able to win back her future once more (assuming the same situation/rules apply).
Thirdly the time is completely off. Rika took a hundred years to escape, whereas Bernkastel was trapped for centuries.
So I find it very hard to imagine that the Rika we know becomes the witch Bernkastel. Frederica Bernkastel becoming the witch Bernkastel is slightly more likely. In any case, some element of Rika is the origin of the witch Bernkastel (unlike the red herring Miyo and Lambdadelta similarities). Whether or not this was through Frederice Bernkastel or starting from a "different Rika".
But that's why I suggested Frederica Bernkastel as a potential antagonist on the meta level. She has all the relevant knoweldge and in terms of personality is quite clearly distached from Rika to the point that she doesn't care for Rika's misfortune or her friends'. (On the other hand, the
cruel personality trait is only something we see in the witch Bernkastel, not so much in Frederica Bernkastel. But honestly, with so little content featuring Frederice Bernkastel it's hard to make that call).
On top of that, the witch Bernkastel would have little reason to do this. She most likely would've grown bored of Higurashi a long time ago (prehaps even resent it, if the logic error did take place on that board) and would not revisit it. But Frederice Bernkastel is a witch in the sea of fragments, but she isn't the Witch of Miracles yet (if she ever becomes it), nor is she (I assume) able to travel between boards. So I'd say:
Frederica Bernkastel learned the full truth about the board with the original end of Higurashi. This allowed her to take control of the board. She then pulled in Rika as a piece and changed rule Y.
(Now obviously this could be completely wrong and likely is, but I'll just continue spouting nonsense and I'm bound to get some things right
)