An important point I’d say would be who is actually commanding the Arab army and who Anatolia and Constantinople itself is assigned to. Mu’awiya is just about to nominate his son as heir to the caliphate and this is definitely going to influence the succession and eventual second Fitna- possibly making the fitna a lot worse as Byzantine territories would provide another army/power base for people to bring into play.
I can’t imagine the new administration just settling into Constantinople- how could a governor live amongst imperial palaces and not claim the imperial mantle himself? Islam is still new enough of a cultural force that I wouldn’t be surprised if there is a strong hellenising tendency in arabs governing Rome. Mu’awiyas Syrian administration was probably all in Greek, and the sole epigraphic trace of his administration is a Greek inscription, which bears a cross before his name- an attempt at Christianising/hellenising Islam might not be off the cards for him. A translatio imperii- whereby instead of being a Greco-Latin empire, Rome would now be Greco-Arab, with military governorships of course reserved for Arab leaders.
What are the chances of Mu’awiya himself moving into Constantinople and seizing personal control? It seems to fit in with his personal ambition but would seriously damage his Arab credibility if he adopted the trappings of a Byzantine emperor, even one that’s doctrinally Muslim.
Imagine an alt Karbala between Muslim Byzantine Emperor Yazid and the more arab forces of Husayn.
As for the 2nd fitnah:
Abdullah ibn Zubayr and Abdullah ibn Abbas (Husayn's father's cousin) as well as other significant companions took part in the siege of Constantinople OTL, campaigning under the (honorary?) command of Yazid.
With Yazid's victory, his fame, glory and perceived ability as a leader would be launched into the stratosphere.
Along with that, ibn Zubayr, Ibn Abbas, ibn Umar etc would have massive influence in Constantinople, probably appointed as governors of Thrace, Bithynia or Smyrna by Muawiyah.
And more generally, immense wealth would flow into the Caliphate, making the people less likely to revolt.
I don't see Muawiyah moving the capital to Constantinople. He was in late 70s/early 80s.
And Syria was where the entire Umayyad powerbase was, even before Islam. And the Syrian Jund/army was one of the largest in the Caliphate.
Moving to Constantinople alienates your entire powerbase, and isolates you. While anti-Umayyad Iraq and the entire east of the Caliphate would be completely out of your control, Rebelling almost immediately...
Ibn Zubayr and Husayn would still reject the notion of a non Sahabi being Caliph over those who lived with the prophet.
With Husayn believing similar.
So if Yazid deals with Husayn's contention in the most unfathomably stupid way possible, as OTL, the outrage would still be massive.
But the Umayyads are in a much stronger position, with much more prestige, wealth and manpower. And not having to worry about Byzantine attacks from the north, thereby not requiring the OTL tribute payments.
So the Umayyads would come back into power sooner.
But the shift to Constantinople would have to be a gradual process, only possible once most of inner Anatolia is conquered.
Unless ibn Zubayr
chooses Constantinople. Instead of isolated Makkah.
Since he would likely have massive respect among the conquering army of Constantinople, due to his status as a senior companion. As well as an esteemed warrior, being part of Yarmuk, conquest of Egypt and being the reason for victory at Sufetula.
Probably having more respect than Yazid himself.....
Especially if ibn Abbas, ibn Umar and other companions of the army of Constantinople join him.
Taking the city, when Yazid is in Syria, to tend to his dying father, and ensure the loyalty of the Marwanids and Syrian army.
This would give him control over the Aegean fleet, and a near impregnable capital.....
Initially, just protesting Yazid's ascension to the Caliphate.
But then Karbala would happen, so that ibn Zubayr would no longer be merely rejecting Yazid., but aiming for the elimination of the Umayyads.
Until Yazid's, death, not much fighting between the two would occur.
With yazid busy keeping Iraq and Madinah/Hejaz as well as Khawarij under control. The sheer distance of Ibn Zubayr would make him difficult to deal with.
Meanwhile, ibn Zubayr would be improving his navy, and perhaps improving his manpower base through recruitment of Slavs and Anatolians
After Yazid's death in 683, the whole Caliphate is thrown into anarchy.
He would be able to use Constantinople's far more strategic position to create a much stronger Zubayrid Caliphate than OTL.
The Zubayrid navy, would quickly take Cyprus, Egypt and Levantine coast.
Using the coast for much more influence in the interior, particularly fairly nearby Damascus via Acre, Tyre and Beirut.
Ideally preventing the Marwanids from even establishing a presence in Syria which was Sufyanid, the Marwanids were mostly in Hejaz, until they got kicked out OTL by ibn Zubayr.
Even if that's not possible, Marj Rahit would end in a Zubayrid victory, with Marwan being slain.
This would result in Qays being more dominant than Yaman.
Iraq would be more difficult to control, due to the sheer distance from Constantinople, and the Anatolian interior not being conquered. Although Makkah was quite far too....
(Makkah is 1250km Constantinople is 1700km)
If ibn Zubayr sent ibn Abbas to Iraq instead of Musab, he should be able to take control over the Shi'ite sentiments in Iraq, since he was the cousin of the prophet, and one of the most senior scholars of the companions.
Instead of Mukhtar ath-Thaqafi, who was claiming for Muhammad alHanafiyyah, despite the latter being against his claim, and not being a companion or son of Fatima
After Marj Rahit, Zubayrids would also have control over the Syrian army, largest in the Caliphate. Giving much greater manpower than OTL, making Mukhtar and the Khawarij much easier to defeat.
(Though Mukhtar might not even rebel in wake of Marj Rahit, seeing all the cards against him....)
Probably ending the fitnah by mid 685. Only a year and a half after Yazid's death, instead of 10...
Meaning, the Caliphate is in civil war for much shorter, making its effects much less potent.
Allowing a quicker return to expansion, as detailed in my previous post.
Ibn Zubayr would probably keep Constaninople as the capital, as it's where his powerbase is strongest.
With Kufa. (Or ideally more strategic Baghdad) as second capital of the east.
Sidepoints
Ibn Zubayr could speak Persian, Ethiopian,
Greek, and Hebrew. Speaking to his slaves in their native languages. As mentioned
https://openresearch-repository.anu...01_Ilhan_Abd_Allah_Ibn_Al-Zubayr_and_2018.pdf
Since he personally speaks Greek and is in Constaninople, this could perhaps result direct Hellenification of the empire?
But overall, once Greeks begin to convert in the late 8th, 9th and 10th centuries, they would probably have a bigger cultural impact on Islam than the Persians.
But since the Muslims now have control over the main mint of the Byzantines, they no longer have to copy Byzantine motifs, and can carry out AbdalMalik style coinage reform and Arabisation in general.
Whether they would actually do that or not is uncertain.
Beyond that, Haiga Sophia would become a mosque, greatly influencing Islamic architecture as a whole...
With Umayyads and Mukhtar defeated, sunnism and Shi'ism probably wouldn't split.
Overall the butterflies this TL would cause would be utterly immense....