The real problem with this "analysis" is that many conceptualize the alleged "persons" as "beings" or "manifestations" and have no idea what their actual professed doctrine IS.
It is disappointing that you would inject into this discussion matters of nuanced distinctions and perhaps spoil the well. It is a disservice to the basic premise of the OP and something that belongs in an exclusively Christian discussion—not in this "Religion" forum. I know you know this and it troubles me you would take the OP as an opportunity to beat your usual drums about the topic. To every thing there is a season...no?
The basics of the Trinity are accessible to anyone who claims to be a Christian. Of the Father, Son, and Holy Spirit,
if we say anything, we must say:
1. The Father is God;
2. the Son is God;
3. the Holy Spirit is God;
4. the Father is not the Son or the Holy Spirit;
5. the Son is not the Father or the Holy Spirit;
6. the Holy Spirit is not the Father or the Son; and
7. they are not three gods, but one God.
No we can, have, and perhaps will wax eloquent on the finer points of the plain statements above—but not herein.
That said, these simple statements amply suffice as starting points,
each of which must be affirmed if one claims "Christian" describes their position.
If you can affirm these seven simple statements, then you have the obvious answer to your direct question as to how I view your claim to be "Christian".
AMR