Would agree that the Mediterranean remains the core of European civilization. The ERE is going to benefit immensely without the Muslims tearing away half of their empire right after they & the Sassanids have beaten each other into a pulp, and continuing to drain away resources which they could've sent against the Slavs in the Balkans or the Lombards in Italy instead. I've said it in past similar threads but you'll probably see
Monothelitism become official Christian doctrine, at least for some time, since it had actually gotten the approval of both the West and East (even if the Heraclians had to twist the Pope's arm into accepting it) and only fell out of favor historically because Syria and Egypt, the regions whose Christian populations it was designed to compromise with, were irretrievably lost to Islam.
That said, it's not going to be easy for the ERE to attempt a Justinian-style reconquest of the rest of the west either. By the 7th century, even without taking Islam into account the Lombards have overrun almost all of Italy, the Visigoths have already driven them out of southern Spain and the Franks are a tougher nut to crack than either of those (probably both of them combined tbh). I could see a revitalized ERE being able to beat down the Lombards and reconquer Italy eventually, since at least they actually have some bases inside the peninsula to start from, but the more distant and powerful Visigoths & Franks will probably be able to remain independent.
We might see a western schism in the form of proto-national churches arising in the barbarian kingdoms, setting themselves apart both politically and religiously from the 'Roman' Church of Constantinople & Rome itself (which will be firmly under Roman imperial authority). Not sure what this would look like in Gothia (the Visigoths have turned away from & suppressed Arianism already), but you might see a Merovingian king who reunites the various kingdoms of Francia assert himself as the head of the Frankish Church or something, with an equivalent to
Gallicanism potentially arising as a compromise position if they ever reconcile with the Romans. (If you really want to go wild with this timeline, imagine lasting Merovingians who go the Holy Blood, Holy Grail/Da Vinci Code route and try to set themselves up as Western Europe's Yamato dynasty by claiming they're semi-divine sovereigns descended from Jesus, heh)
Definitely a much more Christian Africa, especially West Africa. Without Islam rolling in and wrecking all the preexisting arrangements, the Maghreb will likely be thought of as an extension of Southern Europe ITL, dominated by an African Romance Mauri/'Moorish' culture that conceives of itself as the heir to the legacy of Hannibal, Septimius Severus & Saint Augustine and
speaks a language similar to Sardinian. Spared of the 698 sack, Carthage endures as a major city while Tunis remains a village in its shadow. Aside from a Christian equivalent to Mali potentially crashing the Mediterranean economy with an overly lavish pilgrimage to Jerusalem,
it's been speculated that the Malians may also have journeyed to the Americas. Maybe this will be a timeline with a Moorish Brazil and Ghanan/Malian Argentina?
Lastly - historically
the grandson of the last Sassanid Shah was a Christian. And without Islam destroying the Sassanid Empire, Nestorian Christianity remains the majority religion of Mesopotamia, the core of the Sassanids' realm. Perhaps a Christian Persia, further projecting the faith into Central Asia and India (where there are already some existing Nestorians in the form of the Saint Thomas Christians or Nasrani) will also be in the cards? Overall, I'd imagine this will be a much more Christian-dominated world, although of course I'm sure there will be schisms within Christianity itself (at minimum I'd guess at 'barbarian' Christian churches in the north & west, the core Roman-Constantinopolitan 'orthodox' church dominating the Mediterranean, and the Nestorian Church of the East in - well - the east) to keep things 'interesting'.
