the Sassanids only ruled Egypt once, which was 605-629. The Byzantines reclaim the western Levant going south from anatolia, focusing more of their effort there than in north africa in early 629 AD
Well, it wasn't exactly clear, the way the WI was written could also be interpreted as a potential Persian occupation of Egypt.
You say that they reclaim Syria using Anatolia as the springboard. Problem is, Heraclius had very negative personal experience from operations like these, where large Roman armies attacked Persian forces, namely the disastrous defeat at Antioch in 613; the army Heraclius managed to raise in Anatolia following this event was most likely still rather untested, but also perhaps the last large army the empire could field (which meant that risky operations were out of the question); therefore an attack on Armenia, where the Romans could expect less resistance, more favourable terrain, and perhaps hope to force the Persians to withdraw - as it had happened with the campaign of Philippicus. After that, in 624 - 626, he was constantly followed and harassed by Shahrbaraz's forces, who also managed to evade defeat near the river Sarus in Cilicia after Heraclius' successful operations in the east - which most likely prevented him from undertaking any operations in Syria.
To be (remotely) capable of constructing such a scenario as the one described in the WI, one way might be that the Persians achieve a Pyrrhic/very costly victory in the war, where the Romans are forced to cease their operations against Persia for the time being - perhaps Heraclius is less successful in his campaigns and spend some years trying to regroup in Asia Minor, and then Khosrow II's policies trigger the reaction of the great aristocratic families of Iran, resulting in a contest for power. Perhaps if that were to coincide with a more pacifist government at Constantinople (like perhaps a regency headed by Martina, which IOTL seems to have favoured a settlement with the Arabs after their victories), we might, just might, get a situation where a Persian general is in control of Syria and Egypt, and allies himself with the Romans in exchange for a tribute and perhaps grain supplies from Egypt. But this would be a very temporary arrangement at best, and the whole situation would be very hard to achieve I believe.