Tzohar’s kashrut

Rabbi Yaakov Ariel's criticism is about the very existence of private kashrut supervision not through the Rabbinate, a criticism that is well-known, and suddenly all the destroyers of the Rabbinate (the kosher of the Bedzim, their private courts, the converts, etc.) are hanging their lords in the Rabbinate. After destroying it from within! Rabbi Ariel wants to return to a state rabbinate for everyone, which I don't think is likely in the near future.

From here to the principled statement that the food in Zohar's kosher is not kosher?! is not true.
One could say that he doesn't trust it, but not kosher, that's a political statement.

Now that we've entered the discussion, it's interesting why the Bed”tzim, which are also private systems, receive approval from the Rabbinate and Tzohar does not. After all, the Rabbinate could also give approval to Tzohar's kashrut, and then they would be just like the Bed”tzim and everything would be great, wouldn't it? That way our monopolistic regulator (the oxymoron that describes the establishment and status of the Rabbinate) would be preserved to the delight of God and man. Oh, I forgot: unlike the Bed”tzim, Tzohar is not kosher – unequivocally…

With the rabbi's forgiveness, I object to the harshness and cynicism. It does not respect the principled and serious discussion.

First, there is no serious discussion here. If there is – I failed to notice it.
Second, there was no cynicism here. I claim that Rabbi Ariel lied. It seems to me that in the dictionary, saying something untrue = a lie. Does your dictionary say something different?

Since when do Badatzim receive kosher certification from the rabbinate?

They do not receive kosher certification from the Rabbinate. The use of the term kosher is permitted by law only for that which is kosher with the approval of the Rabbinate.