The chemicals for treating lumber changed about 10 years ago to improve safety. Not all PT lumber is the same. Be sure to use something designed for ground contact so they will not rot in 4 or 5 years. The CCA fence post like I used work great on a farm, but they may not be the best for use in a residential setting because of the chemicals used to treat the post.
Looks like you have a lot of trellis to build! Locust post are available in some places. They last a long time. 4X6 post treated for below ground use would last a long time, but are expensive. The CCA post are available at farm supply stores and are reasonable in price.