he doesn't get something like Anatolia but the Levant, Egypt and Caucasus falls to him.
People seem to be forgetting this bit.
Losing the Eastern Provinces (the Levant and Egypt) to the Persians would be devastating yes, however, remember that later on in Roman history that Heraclius was also faced with the same problem and was able to restore the Eastern Provinces despite being in a far less favorable position than the Empire in the late 3rd Century.
Unlike in the early 7th Century, the Balkans and Italy would be more or less secure, perhaps not entirely secure, but a heck of a lot better than in the early 7th Century where half of Italy was occupied by the Lombards and most of the Balkans were occupied by the Avars and Slavs. And while the Western Empire (Gaul and Britannia) is no longer taking orders from the Central Empire, neither are they actively attempting to invade it, so they're nominally a non-factor.
Now let's look at the Persians. They have been able to occupy the Levant and Egypt. Great! Except now they need to militarily occupy those provinces, provinces that aren't necessarily going to be loyal to them. It's essentially the same situation as in the early 7th Century except now they don't have the Miaphysite issue to stir up division between the Eastern Provinces and the Central Imperial Government.
They now have to garrison the various cities in the East, so now a significant portion of their military is tied down in the Roman East. The Persians are now overstretched and have now lost the strategic initiative. Anyone who thinks the Persians will be marching on the African Provinces are kidding themselves. Even if they could, all that would do is tie down even more military resources and make the Persians even more vulnerable to the inevitable Roman counterattack.
So while the Empire isn't in the best of states, it really isn't
that much different from the historical situation. Instead of Palmyra occupying the East it's the Persians and while the Persians are stronger, they also have their own vulnerabilities that can be exploited.
I imagine that Shapur, once Aurelian (or his ALT counterpart) marches east, recognizing that the party is over, comes to negotiate from a position of strength. ALT-Aurelian probably wouldn't accept any deal and the Persians are forced to fight, ALT-Aurelian wins and Shapur gives up the Roman East.
Or Shapur pulls a Khosrow II and refuses to surrender until he's eventually overthrown.
Either way the Romans get their Eastern Provinces back. It's just a matter of how long it takes.