What if Umayyad Crushed Abbasid Revolt?
So the Umayyad Dynasty wipes out their Abbasid rivals. What are the implications? How long could the Umayyad Caliphate potentially have lasted?
Hmm I love this scenario tbh. However since I assume we are just saying the Umayyads won without much difficulty and we don't have to figure out a how to win scenario, then I assume they simply defeated the Abbasid in Khursan, perhaps using an alliance with Harith Ibn Saryaj (whom they promptly kill for being a deviant Shi'i

).
The Umayyad Khilafah is probably my favorite in terms of pedigree and the martial quality it asserted across its vast territory. It was essentially the ultimate Arab state in terms of its ability in warfare and doctrine and because it kept so keenly to tribal ties and security protections.
With that said I will give a hypothetical scenario for a surviving Umayyad Caliphate following a decisive victory over the Abbasid rebels and the Alid Saryaj.
First, following the Umayyad victory the Caliph Abd al-Rahman upon seeing the dissent caused by not allowing more freedom to minorities (which led heavily to the Abbasid revolt) decides to extend security pacts to Zoroastrians (as the Abbasid did) and further remove some of the strength of the tribes in Iran, allowing urban areas for free reign. Reforms like these, will allow a small amount of stability to come and limit the possibility of another movement as vigorous as the Abbasid.
With this said, the Umayyad have a long way to go to continually dominating for a long period of time (Caliphates other than the Ottomans are not known for stability). The constant revolts which will absolutely haunt the Umayyads from Iberia to Khursan to Oman to Cyprus is absolutely frightening to think about. The Umayyads despite having a larger empire to manage and a difficult system, was far better prepared than the Abbasid, mainly because the Umayyad embraced a decentralized ruling system in which tribes of Arabs related to the Umayyad where given autonomy this combined with an Umayyad policy of constant military invasion, raids and conquest (Baqiyah wa tatamaddad, remaining and expanding). The reason this was more stable was that the Umayyads by encouraging constant attack to its north into Europe and south into Ethiopia and East into India allowed these decentralized tribes to fight its own battles while forgetting about the state dominance that the Umayyads held. The only downside would be generals creating their own states and rebelling deep into Europe, Africa or India.
Thus for a a time, the Mediterranean will not recover as unlike the Abbasid, the Umayyad will not relent in aggressive invasions into Europe with its main targets being Sicily, Rome, Sardinia, Majorica, Southern France, Bari & Salento, Crete (owned), Rhodes, Athens, etc basically anything within galley reach of the Mid East. Further the invasion into Anatolia would continue by way of creating Arab buffer zones like the Uqaylid emirate to constantly raid the Byzantine side. The only block in its control was Byzantine strength in the Aegean, the Umayyads were having trouble fighting Byzantine fleets so close to Constantinople and Anatolia becomes increasingly difficult to capture with its mountain ranges and without control of the Aegean to stop flows of troops from arriving from Greece. In Southern Italy, the problem was manpower shortages in taking areas like Salento, as well the population of Italy will only increase and the resistance definite.
The Umayyads would also attempt to continue its slow expansion into the Caucus, with great difficulty. This would likely incur a Khazar-Umayyad war, which could last many years, with a victor not in sight. The Umayyad will also support its vassal Emirates in Pakistan who will be attempting further invasions into India. The result of this could possibly be breakaway kingdoms in India, and or a Tuetonic order situation, quite interesting. To the north in Sogdia, the Umayyad power will likely fade as the populations of Turkish people increase and migrate into Khursan. In Africa the Umayyad like the Abbasid could feed a large economy with slaves captured from wars with Ethiopia and trading with the Swahili states. However this could be a great double edged sword, especially if the treatment is the same as it was under the Abbasid. That being said, without the influence of the Mu'Tazila, it is unlikely that the slave culture that developed under the Mu'Tazila would exist.
The problem of Mamluk slaves could very possibly be avoided altogether. If avoided the Umayyad position as an imperium increases vastly and it's reign prolonged. The way to stop this, would be the increasing martial attitudes prevalent in Arab tribes during the Umayyad period and avoiding the decadent period of the Abbasid. This essentially means that the Turks as an entity would likely move elsewhere than into the Mid East, likely they would become mercenaries for the Emirates in Pakistan, likely gaining control over these statelets. As well, it is always possible for the Turks to invade parts of Khursan and Afghanistan, but likely there will be no great Saljuk empire.
The break off of the Iran is very possible and almost inevitable, however with the Umayyaf centered in Dimshaq (Damascus) they are less threatened than the Abbasid in Baghdad and if so, form buffers around Iraq, Armenia, etc to soften the attacks. Further the position in Syria makes the Umayyad in better position to hold Egypt, North Africa and Iberia than the Abbasid could've hoped for from Baghdad. But also the Umayyad by the same token are more vulnerable to invasions from Europe and will truly be in a dog fight in the chance that a crusader with Byzantine support comes its way during a time of strife.
As far as innovation, there is less as the intellectual culture of the Abbasud period does not occur and the Ulema as a whole is more widespread across the land, as there will likely be no mass centering of power by the more decentralized Umayyad. In the same vein, languages like Aramaic and others like it, would have a better chance of wide use, as the Umayyad were less keen on translating in mass to Arabic, more local polities would speak both Arabic and Aramaic. Plus the location of the Umayyad could soften its time to the Aramiac vast majority of Syria. In Egypt, likely nothing changes linguistically, but Egypt does quite a bit better, while still suffering from desertification which accompanied the Islamic conquest (via mass tribalism and goats), it would benefit as being the main center of an European slave trade and would receive the booty from further conquests into Europe. As an addition, the Umayyad would likely have more trade concentrated around the Red Sea than the Abbasid at the Persian Gulf.
Iberia is perhaps the most difficult, it is far away and decentralization near 100%. Rule here will likely slowly deteriorate. But to keep its power and prolong its rule, the naval dominance in the Mediterranean must be kept. Likely this will be, until the Umayyad suffer a major setback.
Europe as a whole does worse most likely and will suffer a larger period of threats from the south and will not benefit from the relative break that it received during the Abbasid period. Further, trade in the Mediterranean would be seriously out of whack and depressed. Essentially the Umayyads wanted it this way, in some instances it could be considered a massive blockade.
There is probably more you would like, if so, ask. Also I apologize for any spelling or grammar mistakes, this was quite a long post lol.