I'm not familiar with Carrier. I watched a few minutes of his video that you linked, until he said that Paul claimed that Jesus appeared to him and "said he had changed his mind." Granted, I'm sure this is a condensation of what he lays out in his long book, but it is reductive to point of inaccuracy to the New Testament accounts, i.e. the only evidence we have.

Paul seems to have regarded Jesus' resurrection as a resurrection of his physical body but he was ambiguous in his descriptions (e.g. I Corinthians 15:35-44). Clearly the Corinthians were asking questions! The Gospels are less vague. After his resurrection, Jesus was graspable, tangible (Matt. 28:9, Luke 24:39), ate (Luke 24:41-43), and bore scars (John 20:24-28).

It is possible that Paul knew of other dying and rising gods, Osiris, Adonis, Dionysus, other divinities associated with the death and rebirth of the natural world, but that's an argument from silence, since he doesn't mention them.