With more of his forces and focus turned back west, could Justinian get even closer to reunifying the Roman Empire? What would further confrontations with western states, especially the Franks, look like? Additionally, how could you be so certain that the conquests outside of Arabia would be completely unlikely: I find it unlikely that an invading force from Arabia would be unable to use the religious strife of Syria, Egypt, and Africa (with Monophysites, Docetists, and Arians still around in those regions) or the indefensible position of Ctesiphon in Mesopotamia (seeing as scholars like the late Patricia Crone focus on the location of the Sasanian capital as a major factor in the sudden ease that the Arabs had in overruning Iran) to their advantage. I definitely do think that the conquests could be less impactful: could an effective defense be put forward to stop the push into northern Syria?
How long could the Perpetual Peace last do you think? Does it butterfly away a lot of the later conflicts (especially the war of 602-628)
I don’t see a complete restoration of the empire under a single emperor as something feasible, but maybe his invasion of Spain could be more successful with more resources available to him. Personally I would focus on restoring the Danubian Limes ( or at least the Danubian-Drava border), since barbarian tribes there not only threaten communication between the East and West but also one of the main source of manpower for the empire. Anastasius and his predecessors spent lot of efforts trying to secure once again the region and so Justinian should focus on preserving the east before embarking on new expedition in the West.
With a stronger Roman presence in Italy and maybe Spain, Constantinople could decide that keeping the Franks divided could be more beneficial for them, however more importantly they should try to prevent the rise of a hegemonic power beyond the Danube.
As Philip said, this branches of Christianity were either dying or being integrated into the official doctrine at the beginning of the VII century, thus the empire was slowly overcoming this problem, however we should remember that internal strife didn’t cause the collapse of the empire ( and Persia), 25 years of war did. With both empire ready to intervene I think the rise of a hegemonic power in Arabia would be thwarted by both empires.
It’s hard to predict how long the Perpetual peace would last without knowing the course of actions of this alternate Justinian and Cosroe and the exact POD that avoided the war