If we subscribe to events following somewhat the timeline of the OTL ERE-Persian War, (but with the quick fall of Constantinople in 618, as per the POD, substituted for the abortive siege of 626 and the far longer OTL war) all of the damage would be on ERE soil, most of the bloody fighting which happened during Heraclius' invasion of Persia would be butterflied, and as per OTL, the alienated people of the Levant (especially the Jews) and Egypt will in large numbers gladly flock to Persian banners and make Persian control of those areas much less draining to the Persians.
Really, this alt history version of the war is a relative cakewalk for the Persians, and unless the Author of this TL explains, one can only conclude that the Persians would be far less damaged and stretched than the ERE was after the OTL war. The war of this TL is, in fact, a full decade shorter than the OTL war.
And Persia looks far better positioned to ward off Arab invasions than either the OTL Persia and ERE were.