I don't understand why you're focusing on all the nonsensical plot points leading up to the touching & sentimental final moments between Picard and Q. It's the final episode - they stuck the landing and that's all that matters, not the preceding episodes. How we meandered to this point or whether it makes any sense is irrelevant.
The magic of this season of Picard is it was never about plot, or logic, or coherence. This was about Q giving Picard a final gift before he died ... died of, you know. Hold on - why was he dying again? Ah see - I did too, trying to make sense of it. I might go, where's the rest of The Q? His wife and son? Does this contradict Voyager's Death Wish which addressed the Q's state of permanence an inability to die. No no ... these are questions of a fool trying to make sense of something transcendent.
Just let the sublime experience wash over you. Don't think about it - that isn't the writers' intent.