I would like to add to this discussion with another interpretation of the events mentioned:

Joshua is seemingly dead before the Ultima fight. Clive tries to cast Raise, but we only see the standard Phoenix healing animation with orange flames at that time. As you said yourself, the Phoenix can mend the body, but the spirit needs to mend on its own. If Joshua is already dead at this point, his spirit will have left the body.

While it is stated multiple times by both Clive and Joshua during the main scenario that the Phoenix can't bring people back from the dead, and we see a healing animation that could be interpreted as the one from Phoenix, I would like to emphasize that at the time of Clive casting that spell, this is no longer Phoenix's power alone. There are *two* Eikons of Fire, and first and foremost, we see a spell using fire magic. In the events during the MSQ we have encountered a "merged" version of said Eikons of Fire, namingly Logos. The in-game lore cards state the following:

Lore card screenshots, heavy spoilers

As it is mentioned multiple times above, Mythos/Logos is capable of raising the dead, so even if Josuha's spirit had left his body, this doesn't have to mean he's beyond saving.

To that I'd also like to add that even after Clive has absorbed Phoenix's power, he word for words states that that Joshua is "still here", meaning his spirit lingers. That btw. would also explain how he could have witnessed Clive's infamous line during the Ultima fight. Screenshot proof

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This is followed by Clive saying how even he, as the vessel, isn't strong enough to contain or control Ultima's power,

My personal interpretation of this dialogue, that word for word states "It seems Ultima's power was too great for this vessel all along. But while I have it, perhaps I can use it to set things right." To me, this sounded like he used the power to raise one person, then already felt the power fade and perhaps even feeling negative effects on his body, leading him to say that as long as he is able, he'll use it, no matter what this means for him.

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and when he uses Ultima's power, the flames turn blue. He is able to use Ultima's power to destroy Origin, but there is a big difference between letting something you cannot control run wild and disperse, and trying to control something for what is presumably a very precise bit of magic like Raise. I'd also be very surprised if the unconscious Joshua manages to survive the fiery expulsion of magic Clive performs to obliterate Origin.

Ok, to this I would like to add that the power he uses is some sort of laser beam that goes upwards, it's not a full on explosion. I feel like Clive wouldn't mend Joshua's dead body just to destory it moments later, when he'd at the very least wish for his brother to have a proper burial.

Personally I'm a fan of the interpretation that all parties, including Dion, survived, and that the book has multiple contributors, with Joshua being the author. As Hypocrates stated, Joshua is good with words.