Before the Battle of Manzikert Antioch was part of the Eastern Roman Empire, but the rest of the Levant is a different story. If the oath was referring to all former Roman territories the areas that the Crusaders would be obligated to return would stretch all the way to the southern parts of Egypt. The Crusaders did not care about the oath very much, and Antioch was not returned, instead, Bohemond of Taranto founded the Principality of Antioch. Was Constantinople still interested in the Levant? Did Emperor Alexios have any way to enforce this oath?
Antioch can be more directly tied to the oath since it was recently controlled by the Eastern Romans, and John II forced the Principality to become a vassal state a few decades after the Crusade. I'm more interested in the territories which hadn't been Roman for centuries.
The background for this is essentially, as you mentioned:
“Each of the leaders was required to swear an oath…which contained an undertaking to hand over to Alexios any captured towns which had previously belonged to the empire.” (Harris, 63)
Sounds simple enough! But as you’ve noted, it’s not exactly clear which territories Alexios meant. Apparently, the oath included all of Anatolia, up to and including the borders of Byzantine Antioch. It apparently did not apply to anything further south, beyond the borders of Antioch.
All the crusaders eventually swore the oath, although some, like Raymond IV of Toulouse, were extremely reluctant. The oath temporarily turned the crusade into an extension of the Byzantine army, which was guided by Alexios’ generals and attacked Byzantine objectives, like Nicaea and Dorylaeum. Clearly, everyone agreed that the territories in Anatolia would be restored to the empire. They had been part of the empire just before the crusade, and in fact that was the reason Alexios asked for help in the first place. Anatolia was a big place full of Greek-speaking Christians, and more importantly it produced a lot of food and revenue for the empire. The crusaders weren’t interested in keeping any of that.
The crusaders arrived at Antioch in October 1097, but most of the Byzantine forces had stayed behind in Anatolia, so they were on their own. The siege was extremely difficult, but they managed to take the city in June 1098 - and they were immediately besieged themselves, by a Seljuk relief army from Mosul. The crusaders were stuck in the city for another six months. Some of them managed to escape and fled back toward Constantinople, including Stephen of Blois. On the way, Stephen met Alexios himself, who had heard what was happening and was actually coming to help them, but Stephen convinced him the situation was hopeless, the crusaders would certainly be defeated, and there was no point continuing. Alexios turned back.
The crusaders did end up defeating the Turks, but they definitely knew that Alexios had turned back. From the Byzantine perspective, Bohemond was the one who broke the oath, but for the crusaders, it was Alexios who had betrayed them. Why should they keep their oaths to him? So it’s probably more accurate to say that the crusaders did care about the oath, and if Alexios had arrived in 1098, they probably would have handed Antioch over to him. Bohemond might still have ended up in charge, as a Byzantine governor rather than an independent prince. But the way things turned out, the crusaders considered Alexios the oath-breaker, so they kept Antioch for themselves.
Did Emperor Alexios have any way to enforce this oath? He did! As long as Byzantine troops led by Byzantine generals were escorting the crusaders around Anatolia toward Byzantine targets like Nicaea, the oath was enforced. Cities were returned to the Byzantines directly, or held by a small crusader force until the Byzantines arrived. Alexios didn’t want to stretch his army too thin though, so they didn’t go all the way to Antioch with the crusaders. If he had gone all the way to Antioch, yes, both he and the crusaders certainly would have enforced the oath.
Would he have enforced the oath further south, including Jerusalem? Apparently no. Even if Alexios had arrived in Antioch. the Byzantines were not interested in the Levant at all. Jerusalem was strategically completely meaningless to them - it was far away and hadn’t been under their control for 400 years. We can see from their actions in the years after the First Crusade that they still weren't interested in Jerusalem even after the crusaders captured it. The Byzantines forced Antioch to become a vassal of the Empire, as it should have been (in their minds) in 1098, but while they made alliances with and intermarried with the other crusader states, they never tried to impose their control over them, like they did in Antioch.
Sources:
- Jonathan Harris, Byzantium and the Crusades (Hambledon and London, 2003)
- Thomas Asbridge, The First Crusade: A New History (Oxford University Press, 2004)
- Thomas Asbridge, The Creation of the Principality of Antioch (Boydell, 2000)
- Andrew D. Buck, The Principality of Antioch and Its Frontiers in the Twelfth Century (Boydell, 2017)