The thing is though, Persia WOULD be weakened if they had such a total victory - the Byzantines would take a long time to fall, and Greeks and Christians are likely to give them quite a bit of trouble. In other words - think the reverse of OTL situation, with Persia in Byzantium's OTL role.
Though I agree that Persia would be weakened by the extensive war againest the Byzantines, I don't think that it would be as hopelessly weak as you describe.
Without the humiliating defeats at the hands of Heraclius in Azerbaijan and at Nineveh, Khusrau's position would remain strong, or at least strong enough to prevent the chain of events that begun with Kavadh's liberation and coronation, and ended with the collapse of the Sassanid Empire.
And instead of being demoralized by the defeats againest Heraclius and the general anarchy following Khusrau's death, the Persian army would still be at the peak of their morale due to their recent victories againest the Byzantines. And their leadership would be stronger too.
That could make a lot of difference - even if the Arabs do manage to take Syria, Mesopotamia and Egypt, then, with some proper leadership and without the anarchy that befell Persia IOTL, the Persians could successfully defend areas like Fars, Azerbaijan, Khoresan, and perhaps even Kerman againest the Arabs.
In such a scenario, they would retain a viable empire, just like Byzantium IOTL.
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However, the Arabs still have the advantage that the Persians are still concentrating their troops in the recently conquered territories, and to a lesser extent, in Transoxiana.
Heraclius managed to archieve his OTL victories thanks to Khusrau's tactical mistake of having almost no forces defending Mesopotamia and the other heartlands of the Persian Empire.
And ITTL, Khusrau would only be more overconfident, and he would certainly not expect the Arabs to become a serious threat, ever.
And not only does barely defended Mesopotamia border the Arabian desert - Khusrau had also made the crucial mistake of destroying the Lakhmid kingdom for such a trivial issue as the Lakhmid king's refusal to let Khusrau marry his daughter.
The Arabian Lakhmids were loyal vassals of the Sassanids, and had their kingdom remained strong, then the Arab conquest of Persia would have taken a lot longer, and it
might even have been prevented - even in a scenario that
does include Heraclius.
But IOTL, the remnants of the Lakhmids were defeated by the Muslims and incorporated in the Caliphate without too much effort, which only made their conquest of Mesopotamia and Persia easier. And ITTL, the Lakhmids won't be able to do much againest the Muslim invasion either, thus leaving a rather serious weak spot in the Sassanid frontier, right in an area that would be among the first to be attacked by the Muslims.
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So, in the end, I'd say that things could go either way, with the destruction of Persia, the (near-)destruction of the Caliphate, and the survival of both empires being possebilities.
But exactly what will happen will depend on a few factors, such as wether Khusrau II will still be alive when the Arabs invade, how he will handle the Arab invasion if he is, and who his successor is and what he'll do if he isn't.