So did Palpatine want Anakin to kill him?
Palpatine clearly expected Knightfall Vader to eventually challenge and overthrow him. It's a weird self-sacrificing angle that also applies to all Banite Sith, but it's especially bizarre with Palpatine because we then learn that he intends to become some sort of universal God.
Did he plan to somehow keep Vader under his thumb even if he hadn't lost his potential? Delusional. Was he going to kill him before he grew that powerful? Obviously not or why bother turning him? Was he planning to try to essence transfer into Anakin? Extremely risky given Anakin's innate power.
Did he change his mind and adopt the God-Emperor plan after Vader's injuries? If that were the case why would he want to turn Skywalker, and then allegedly want to rule forever with the Skywalkers as a "dynasty" by his side (at least in Legends)? An apprenticed Luke would clearly eventually try to overthrow him, and have a very good chance of succeeding.
So maybe finding a successor was plan A, becoming God himself was plan B, and we just ignore the ruling forever with Skywalkers by his side part?