Why does the Church pay its institute and seminary teachers, isn’t that priestcraft?

Good question.
Priestcraft isn’t necessarily receiving money for teaching the Gospel. ”Priestcrafts are that men preach and set themselves up for a light unto the world, that they may get gain and praise of the world; but they seek not the welfare of Zion” (2 Nephi 26:19, The Book of Mormon). Priestcraft is when a person preaches the Gospel to build himself or herself up, not to build up the kingdom of God.

However, there is a caution in the scriptures that those that receive money for preaching the gospel should be aware of. “But the laborer in Zion shall labor for Zion; for if they labor for money they shall perish” (2 Nephi 26:31). A person’s intent must be to build up Zion, not to make money.