Oh, please! Teutonics at 14th century were fresh and rising; Byzantium at 7th century was a living corpse.
"Fresh" and rising doesn't exactly mean "Teuton über alles".
It's not the place to discuss your TL anyway, but you're not in the best position to be condescending on these matters. Period.
As for Byzantium in the VIIth century...
Not only, by the grace of chronology, you'll notice that Islamic conquests were already a thing by then. And that the OP, kind of butterfly them.
And even if weakened by a large war, the empire still demonstrated its possibilities during Heraclius' reign : reconstitution of an army from scratch, making Persian nearest provinces clients,
Ekhtésis as a conciliation measure with different denominations (with the negative consequence of pissing the pope, but at this time, nobody really cared. It wasn't the first time, and imposed exile or new election generally dealt with that).
The fact Arabs didn't took Anatolia, that at the contrary of Palestine and Egypt was subject to an actual defense plan, point again the imperial capacities.
In all fairness, Byzantine Empire was in better shape than the late Visigothic kingdom that experienced a series of coups (failed or not) without the excuse of Persian wars or Arab conquests.
While not being the hellhole of ineffectivness often depicted, they didn't prooved being "fresh and rising".
There is a big difference in imposing certain decisions than in throwing their whole church on them. Franks would have never accepted some rigid customes of the Byzantine Church, not to say Visigoths.
So rigid that the emperors actually preferred concede many points than risking to have different denominations rush against them.
At this point, I honestly don't know what you're saying : maybe BG would have a better answer than I on this.
But roughly : the difference between Greek and Latin church are at this point, minimal.
You would have maybe more similarities between Latins churches, each being ruled by their respective kings, but then again Byzantines churches (I mean "official" one there, actually included Roman church that was the main common point of Latin religious entities).
Periods with actual religious conflict between Latins and Greeks, are almost always accompanied if not dominated by political issues rather than theological. Long story short : King and councils represent Church integrity, and by replacing part of both (whatever by the kingdom being deprived of a province and/or bishops being replaced) this integrity is compromised.
Actual theological differences or issues, on the other hand...Were pretty much absents.
The first real divide came from Carolingian Empire, in the IXth century, with by exemple the famous
Filioque. As in, the empire that is likely to be butterflied with no Islam.
I think that after the end of the Byzantine-Sassanid war they had the same chances of recovering (or not) that the Byzantines in the long term. Arabs prevented us to check which of both could have recovered first.
They could have recovered. With time.
But while Heraclius' Empire still held together, if weakened by a long and harsh war; Persia was quite divided and ruled by a child king, his co-ruler and knew some revolts of its own.
Byzantium was clearly in better shape (It's basically why it survived).
The migratory activity in Central Asia during the 7th-8th centuries was conditioned by the Islamic expansion there. Without them, you can't guess if some migrations (Turks) could have anticipated,
The steppe migrations were more likely conditioned by climatic changes, as they were always. Reduction of pastures somewhere, being pushed by other peoples, etc. In fact, the process already began in the VIth century, without real Islamic influence on it (as for Islam not being a thing then).
In this regard persian politics towards Central Asian peoples isn't going to be that much different from Arabo-Islamics : they used them as mercenaries since quite a long time already.
especially if they would have considered the Sassanids easy prey, as you suggest.
At the contrary of Arabs, that had already an imperial structure (even if based on tribal features) due to being long influenced by both Byzantines and critically Persians, Turkic peoples still used tribal and "confederal" features.
If they (Maybe an offpsring of Köktürks) invaded Persia and settled there, more likely they would be assimilated as Seljuk were greatly Persianised IOTL.
However, they can't hold it even before the Arab expansion; any eventual new try on Spain was too challenging, I guess.
Do you know about
Roman-Persian wars?
As in, a really important, ressource and financial gap, and devastating conflict?
I strongly suggest you to make a quick search about it, beggining with
this.
Let be clear : surprisingly, a global empire can't fight everywhere. It doesn't mean Visigoths were super-uber warriors, but that the Persian wars diverted too much focus.
Even with that, regular reconquests did happened up to the early VIIth century.
In fact, a non-negligible part of Visigothic troubles were due to Byzantine intervention.
You overlook the fact that Byzantium was internally very unstable since the Justinian era. The Arab conquests at least provide some internal unity against a common and dangerous enemy and also deprived the Empire of their more conflictive provinces.
So, I think that without the Arab conquest, it's possible that Byzantium had great chance of collapsing because internal infight, you can say 'balkanizing' in different kingdoms or so.
So far, most of the inner conflicts weren't about creating smaller kingdoms but about a claimant to the imperial throne revolting. Not about creating smaller kingdoms.
Unless you argue about denominational "nationalism" with Jabobits and Monophysits? As BG tried to point out in other threads, you didn't had a reject of imperial political integrity, but rather the reject of too dogmatic-minded emperors (and Heraclius prooved that he wasn't exactly that)
In Spain there is an expression in politics that say 'un partido bizantino' (a byzantine party) to refer a political party that can't success because of continued internal conflicts.
Are we about using expressions now, critically when they appeared after Byzantine Empire was dead and buired? *Shurg head in disbelief*
There's a french saying "Build castles in Spain" to refer to dream and futile plans. Does that mean there is no castles at all in Spain.
The Sassanids were not going to collapse. The civil war was over when Yazdegard III took control of the throne.
Maybe not to collapse, but certainly much divided and not posing an immediate threat, certainly not with an eight-year-old ruler.
Furthermore, with the presence of a co-ruler (Hormizd V) and without Arab threat to relativly unify Persians, I'm not sure the important deep divisions wouldn't last (as the revolt apparently happening in 634 preventing to exploit victory at the Battle of the Bridge)