The Byzantines did resurge towards Syria IOTL in this era, right? I still don’t think that would mean they could re-establish the empire at the start of Heraclius’ reign, though—if nothing else an independent Egyptian regime could drive them out.
Yeah, the Byzantines invaded the Mashriq multiple times, with the peak being John I Tzimiskes' invasion, conquering all of Syria and Upper Mesopotamia. Yet, the Byzantines being the Byzantines, Tzimiskes was assassinated upon his return to Constantinople (despite having saved the empire against a Russo-Viking-Bulgar invasion just a few years prior).
Then Basil II takes power and after finishing off the civil war in Anatolia, he rather pragmatically decides to create defensible borders in the east instead of going for an ambitious lightning campaign in the east. The former was more sensible, but he probably could have tried the latter if he were more typical of Byzantine leaders.
Politically there are a lot of obstacles to a Byzantine resurgence. But the Byzantine "war machine" if you will certainly would have been theoretically capable of such expansion, if diplomatic and political factors did align. Such expansion might have been possible if Tzimiskes survived, probably by discovering the plots of Basil Lekapenos (his assassin, who was successfully banished by Basil II).
...Of course, I suppose one could argue a similar thing for the Abbasids, who certainly had the economic base to reconquer their former lands, but were politically faced with too many enemies on all sides. Frankly, though, the Abbasids have a decent, if slim chance too if they had a couple more soldier-Caliphs after al-Muktafi. I think a plausible TL could be created with either a Byzantine resurgence, an Abbasid resurgence, or seeming paradoxically, both -- they were close trading partners and for the most part, shared mutual enemies.