Jesus functioned as a priest primarily when he offered himself as a sacrifice for sin. This act is central to Christian theology, as it is believed that Jesus fulfilled the role of a high priest by offering himself as the ultimate sacrifice for humanity's sins, thus reconciling humanity with God.
While other actions you mentioned, such as instituting the Lord's Supper and teaching about prayer, also reflect aspects of his priestly role, the sacrificial act is the most significant in terms of his function as a priest.