We know little about this period. Its an interesting POD.
First, what is left of the East Romans/ Byzantium. The Persians ITTL can't get to Italy. They could get to North Africa but are probably exhausted by the effort of taking Constantinople plus there is still Greece to deal with. Probably the Western Exarchates produce a new Emperor, who manages to create a hodgepodge Western Empire that includes parts of Italy, North Africa, and Greece. This has some chance of surviving for quite a while if they can find a way to deal with the Lombards and/ or the Franks, a big if. It wouldn't be called the "Byzantine" empire and would need to have a symbiotic relationship with the bishops of Rome.
Second, the effect on the Arab conquests and Islam. Islam still exists iTTL. Persia is still exhausted by the war and the Arabs could still conquer it anyway. The significant difference is that without the East Romans/ Byzantines in Anatolia, they expand into Anatolia and probably not into North Africa (completely different allocation of lines of effort by the Arabs and the Byzantines/ Romans in this scenario). There is also a chance of peaceful conversion of the Persian Empire to Islam under a later Shah. Or Zoroastrianism could mutate into a more popular religion, OTL it was really a religion for the Iranian elite.
Also keep in mind that the Sassanians were even more prone to fighting civil wars among themselves than even the Romans were. I think there is a good chance of getting something like the OTL Caliphate anyway, they always had more difficulty in expanding against the East Romans/ Byzantines.