When Jesus said "It is finished" (John 19:30) did the High Priest also say it was finished at the end of the Passover slaughter

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I’m looking for a historical source on any Jewish sacrificial ritual (e.g., Passover, Day of Atonement) in which the high priest would cry something like, “It is finished.” I’ve seen a number of blogs saying that such a thing happened, but I cannot find anything like it on Sefaria.org or in more reliable Bible commentaries. I also have seen a few online discussions on what the Hebrew equivalent of τετελεσται would be, and all the answers seems somewhat speculative. With that in mind, I’m beginning to believe that there is no well known tradition of a priest saying “it is finished” at the end of a ceremony.

Part of the reason why I am asking is because I am wondering if Jesus said “I thirst” (John 19:28) because His tongue was cleaving to the top of his mouth (Psalm 22:15), and Jesus needed some water to better enunciate “it is finished.” When He said “Eloi, Eloi, lama sabbachthani” those standing at the base of the cross could not understand what He was saying (Matthew 27:46).