The Last Supper dialog was already well established. It had been mentioned in three Gospels and in 1st Corinthians. John’s Gospel was written 20-30 years after these other accounts (it is best assumed) and so He wanted to “fill in the gaps”, so to say.
With this in mind, John’s Last Supper discourse seems to indicate an annointing of the priesthood, in some people’s opinion. Some of the words that John used pointed to priests. I might get these wrong but, “Meros” (in Greek), for example, during the footwashing was used for inheritance (“If I don’t wash your feet, then you’ll have no inheritance in me”). This word, Meros, was used to describe the Levite priests’ inheritance in the Mosaic Covenant. Also, the footwashing (and headwashing) was part of Aaron and his sons’ initiation into the priesthood. And any time a priest entered the Tent of Holies, he had his feet (and head) washed. There are other terms that Jesus used that pointed towards priestly things (i.e. the “dwellings” that Jesus is preparing in His Father’s House is the same term that the Historian Josephus used for the “dwellings” that the Levites lived in while servicing the Temple - Jesus’ Father’s House - in Jerusalem.
Finally, the “priesthood” context is further zeroed in on when Jesus breathes on the Apostles and gives them the Holy Spirit. What is the context of this gift of the Holy Spirit? Forgiveness. “The sins you forgive, are forgiven. The sins you retain, are retained”. In the Old Testament, Leviticus chapter 5, the Levite priests were instrumental in the forgiveness of the Israelites offenses.