The Trinity claims that there is one “being,” which they call God, and three “persons”: the Father, the Son, and the Holy Spirit.
These terms use a special Christian vocabulary that differs by interpretation. Thus we must understand this concept using clear terms. I will use the term actor.
According to the trinity the father is not the son, the son is not the holy spirit and the holy spirit is not the father.
Jesus was born and walked on earth; the Father did neither. Thus, they differ in action.
The same actor cannot both perform an action and not perform it. Since the Son acts where the Father does not, they are separate actors.
3 separate actors that are all divine are 3 deities.
One could make the argument that these separate actors are “one being” by appealing to a shared “essence” or property but such an argument is incoherent.
It amounts to saying that all humans on earth are the same human because we all share the same “human essence”
This argument is identical to Hinduism. Hindus believe that 3 deities brahma, vishnu and shiva that are all the essence of a deity they call brahman, and they believe all their other deities are from that same essence and come from these 3 deities.
People who believe everything that exists has the same essence could worship random statues, men, women, animals, objects and claim to be monotheists because of this abstract belief in a “shared essence”
Neither can you divide the actions into “divine actions” and “non divine actions” in order to explain away why they have differences in actions since any difference in action implies a different actor since the same actor cannot do an action and not do the same action.