My own words about person in regards to the trinity was that it seems something like “facets of God’s personality” and in my other post I mentioned how the catechism defines it which is “the term “person” or “hypostasis” to designate the Father, Son and Holy Spirit in the real distinction among them.”
It is almost like an avatar. However, avatars are physical manifestations of 1 God. I think Christ is the only one that qualifies as anything like an avatar (in fact, I’ve heard others refer to him as one). However, people can “feel” the Holy Spirit and they pray to the Father…perhaps they are more like the non-manifesting avatars. Also, I’m not sure how distinct avatars are compared to the trinity.
Did that help?