what trouble really i have read the material and especially the monophysite response to the Arab invasion by John Moorhead what danger was there in? Heraclius did not implement his compromise by force quite the contrary also most of the population wouldn't care/ know about the heresy i will quote some parts of a long post of mine
As for sources in the 7th century few of them from these groups have survived, but in Heresies in the early Byzantine Empire Imperial policies and the Arab conquest of the Near East Rashad Odetallah quoting E. R. Hardy stating how for most of the territory the conflict would not have existed
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so I am in good faith asking what is the danger here?
your applying our modern views on him, and while this would have merit in say 624 this was not case in 630 Heraclius was not seen as a usurper and while he did arguably make the war worst he won it and was seen and he presented himself as the empire savior /deliverer were chanted ( a good read on this is Heraclius by Walter E. Jr. Kaegi) also why would a rebellion happen? in the otl Heraclius lost hard he lost Syria and Egypt was falling when he died and yet we had no revolt during his reign Heraclius did face a lot of criticism in his later years but again the man lost Syria and was losing Egypt yet one revolted if no one did after a massive disaster like Yarmouk , and losing Babylon fortress why would some one for something less?
he mostly got it for his dad dying wish sure Valentinus played a role but there was no civil war no one wanted Heraklonas and Martina in power and like mentioned the instant Valentinus tried to userp Constans II he was killed if the biggest dynastic issue was exiling two people despite the arabs having conquered Syria and egypt now it shows the dynasty was still secure not the other way around.
I don't but I am basing myself on the otl where I am against the state the rise of Islam was the worst-case scenario and yet from its start in 634 we have to wait until 647 for any major revolt to start with Gregory