Hi Gandalf. To answer your question, no, the Trinity does not imply that Jesus is literally the Father. The Trinity Doctrine asserts that there are three separate persons, the Father, the Son, and the Holy Spirit, who each are coequal and coeternal with one another. The three together make up a single entity of what God is. Jesus is fully God, but a separate person. The Father is fully God, but a separate person. The Holy Spirit is fully God, but a separate person.
That is why if you hold to the doctrine of the Trinity, you would not want to imply that Jesus is the Father, because they are separate persons according to it. Also, I just read your post #1602. In it, you actually described what Trinitarians believe. If Trinitarians didn’t claim that all three of those persons were the same God, then they would be worshipping three Gods instead of one.