The eminent scholar of Ethiopian studies/languages Wolf Leslau, in his Comparative Dictionary of Ge’ez, gives the definition of kwannana as to “regulate, rule over, have dominion, govern, judge, pass judgment, pass sentence, plead, convict, condemn, punish…” In discussing the etymological origins of the word, Leslau rejects Grimme’s suggestion (1901) that it from Hebr כנן (‘establish’), as this is a polel stem. He settles for the possibility that it may be taken from “Semitic kwn (Heb. ken, Syr. kawwen ‘erect, admonish’) with reduplicated last radical.”
I’d like to suggest what is, in my view, a better candidate: it is instead taken from חנן. The hithpael of חנן, to “ask for/seek grace, kindness; to plead,”* coheres well with the meaning of takwanana, “plead, press for justice.” The hithpael here merely “[seeks] what the simple stem designates”*: “to show favor/be partial to,” which puts us closer to the idea of “judgment” that most of the meanings of kwannana seem to revolve around—at least those instances in the Hebrew Bible where !nx is used in a context where one figure or one group is favored over another, or is beseeching someone to favor them over another.
Yet all of the occurances of חנן in the Hebrew Bible—if accurate to say that some of them have ‘judicial’ hints—only have connotations of positive judgment. It’s not clear whether any more general judicial connotations can be teased out of this.