Sendbrief means open letter.
What is the connection between "ecclesiastical court" and "letter" in the formation of Sendbrief?
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Sendbrief doesn't really mean "open letter", at least not in contemporary German.
"Send" also absolutely doesn't mean today ecclesiastical court. Don't know where you got this from.
"Sendbrief" is an archaic expression for open letter which would today be expressed with "offener Brief" (so quite the literal translation from the English expression). Because in former times it was mainly clerical organisations that sent around open letters, "Sendbrief" might today still be used as an expression for an "open letter from the church". A commonly known example is "Luthers Sendbrief vom Dolmetschen" - An open letter to address criticism of his liberal transscription of the bible.
Both Sendbrief and Send are historical clerical terminology and not used in contemporary German outside clerical organisations (wouldn't even know whether they are still used inside that organisations). Both expressions stem from the verb "senden" (to send).
As others have noted, "Sendbrief" (and also the more common "Sendschreiben") is from the verb "senden".
"Send" in the sense "ecclesiastical court" is a Germanised form of Latin (ultimately Greek) "synodus". The German word is, as the DWB puts it, "in neuerer zeit mit der sache ausgestorben".